Adaptive dynamical networks. (English) Zbl 1532.81014
Summary: It is a fundamental challenge to understand how the function of a network is related to its structural organization. Adaptive dynamical networks represent a broad class of systems that can change their connectivity over time depending on their dynamical state. The most important feature of such systems is that their function depends on their structure and vice versa. While the properties of static networks have been extensively investigated in the past, the study of adaptive networks is much more challenging. Moreover, adaptive dynamical networks are of tremendous importance for various application fields, in particular, for the models for neuronal synaptic plasticity, adaptive networks in chemical, epidemic, biological, transport, and social systems, to name a few. In this review, we provide a detailed description of adaptive dynamical networks, show their applications in various areas of research, highlight their dynamical features and describe the arising dynamical phenomena, and give an overview of the available mathematical methods developed for understanding adaptive dynamical networks.
MSC:
| 81P68 | Quantum computation |
| 68M10 | Network design and communication in computer systems |
| 68T05 | Learning and adaptive systems in artificial intelligence |
| 62M45 | Neural nets and related approaches to inference from stochastic processes |
| 91D30 | Social networks; opinion dynamics |
Keywords:
adaptation; dynamics; networks; co-evolutionary; complexity; neuronal plasticity; rewiring; event-based adaptation; Multiscale; cooperation; opinion formation; mean-fieldReferences:
| [1] | Newman, M. E.J., The structure and function of complex networks, SIAM Rev., 45, 2, 167-256 (2003) · Zbl 1029.68010 |
| [2] | Porter, M. A., Nonlinearity Networks: A 2020 Vision, 131-159 (2020), Springer International Publishing: Springer International Publishing Cham, (Chapter 6) |
| [3] | Holme, P.; Saramäki, J., Temporal networks, Phys. Rep., 519, 97-125 (2012) |
| [4] | Holme, P., Modern temporal network theory: a colloquium, Eur. Phys. J. B, 88, 9, 1-30 (2015) |
| [5] | Gross, T.; Blasius, B., Adaptive coevolutionary networks: a review, J. R. Soc. Interface, 5, 20, 259-271 (2008) |
| [6] | Gross, T.; Sayama, H., Adaptive Networks (2009), Springer-Verlag Berlin Heidelberg |
| [7] | Gerstner, W.; Kempter, R.; von Hemmen, J. L.; Wagner, H., A neuronal learning rule for sub-millisecond temporal coding, Nature, 383, 6595, 76-78 (1996) |
| [8] | Caporale, N.; Dan, Y., Spike timing-dependent plasticity: A hebbian learning rule, Annu. Rev. Neurosci., 31, 1, 25-46 (2008) |
| [9] | Markram, H.; Lübke, J.; Frotscher, M.; Sakmann, B., Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs., Science, 275, 5297, 213-215 (1997) |
| [10] | Bi, G. Q.; Poo, M. M., Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type, J. Neurosci., 18, 24, 10464-10472 (1998) |
| [11] | Abbott, L. F.; Nelson, S., Synaptic plasticity: taming the beast, Nature Neurosci., 3, 11, 1178-1183 (2000) |
| [12] | Bi, G. Q.; Poo, M. M., Synaptic modification by correlated activity: Hebb’s postulate revisited, Annu. Rev. Neurosci., 24, 1, 139-166 (2001) |
| [13] | Meisel, C.; Gross, T., Adaptive self-organization in a realistic neural network model, Phys. Rev. E, 80, 6, Article 061917 pp. (2009) |
| [14] | Lücken, L.; Popovych, O. V.; Tass, P. A.; Yanchuk, S., Noise-enhanced coupling between two oscillators with long-term plasticity, Phys. Rev. E, 93, 3, Article 032210 pp. (2016) |
| [15] | Hoppensteadt, F. C.; Izhikevich, E. M., Oscillatory neurocomputers with dynamic connectivity, Phys. Rev. Lett., 82, 14, 2983-2986 (1999) |
| [16] | Du, C.; Ma, W.; Chang, T.; Sheridan, P.; Lu, W. D., Biorealistic implementation of synaptic functions with oxide memristors through internal ionic dynamics, Adv. Funct. Mater., 25, 27, 4290-4299 (2015) |
| [17] | John, R. A.; Liu, F.; Chien, N. A.; Kulkarni, M. R.; Zhu, C.; Fu, Q. D.; Basu, A.; Liu, Z.; Mathews, N., Synergistic gating of electro-iono-photoactive 2d chalcogenide neuristors: Coexistence of hebbian and homeostatic synaptic metaplasticity, Adv. Mater., 30, 25, Article 1800220 pp. (2018) |
| [18] | Pickett, M. D.; Medeiros-Ribeiro, G.; Williams, R. S., A scalable neuristor built with mott memristors, Nature Mater., 12, 114-117 (2013) |
| [19] | Waldrop, M. M., Neuroelectronics: Smart connections, Nature, 503, 22-24 (2013) |
| [20] | Ignatov, M.; Ziegler, M.; Hansen, M.; Petraru, A.; Kohlstedt, H., A memristive spiking neuron with firing rate coding, Front. Neurosci., 9, 376 (2015) |
| [21] | Hansen, M.; Zahari, F.; Ziegler, M.; Kohlstedt, H., Double-barrier memristive devices for unsupervised learning and pattern recognition, Front. Neurol. Front. Neurosci., 11, 91 (2017) |
| [22] | Birkoben, T.; Drangmeister, M.; Zahari, F.; Yanchuk, S.; Hövel, P.; Kohlstedt, H., Slow-fast dynamics in a chaotic system with strongly asymmetric memristive element, Int. J. Bifurcation Chaos, 30, 08, Article 2050125 pp. (2020) · Zbl 1448.37126 |
| [23] | Schuman, C. D.; Potok, T. E.; Patton, R. M.; Birdwell, J. D.; Dean, M. E.; Rose, G. S.; Plank, J. S., A survey of neuromorphic computing and neural networks in hardware (2017), arXiv:1705.06963 |
| [24] | Jain, S.; Krishna, S., A model for the emergence of cooperation, interdependence, and structure in evolving networks, Proc. Natl. Acad. Sci., 98, 2, 543-547 (2001) |
| [25] | Jain, S.; Krishna, S., Crashes, recoveries, and “core shifts” in a model of evolving networks, Phys. Rev. E, 65, Article 026103 pp. (2002) |
| [26] | Jain, S.; Krishna, S., Graph Theory and the Evolution of Autocatalytic Networks, 355-395 (2002), John Wiley & Sons, Ltd, (Chapter 16) |
| [27] | Kuehn, C., Multiscale dynamics of an adaptive catalytic network, Math. Model. Nat. Phenom., 14, 4, 402 (2019) · Zbl 1418.37086 |
| [28] | Gross, T.; D’Lima, C. J.D.; Blasius, B., Epidemic dynamics on an adaptive network, Phys. Rev. Lett., 96, 20, Article 208701 pp. (2006) |
| [29] | Proulx, S. R.; Promislow, D. E.L.; Phillips, P. C., Network thinking in ecology and evolution, Trends Ecol. Evol., 20, 6, 345-353 (2005) |
| [30] | Sawicki, J.; Berner, R.; Löser, T.; Schöll, E., Modelling tumor disease and sepsis by networks of adaptively coupled phase oscillators, Front. Netw. Physiol., 1, Article 730385 pp. (2022) |
| [31] | Berner, R.; Sawicki, J.; Thiele, M.; Löser, T.; Schöll, E., Critical parameters in dynamic network modeling of sepsis, Front. Netw. Physiol., 2, Article 904480 pp. (2022) |
| [32] | Gautreau, A.; Barrat, A.; Barthélemy, M., Microdynamics in stationary complex networks, Proc. Nat. Acad. Sci. USA, 106, 22, 8847-8852 (2009) · Zbl 1203.91243 |
| [33] | Tero, A.; Takagi, S.; Saigusa, T.; Ito, K.; Bebber, D. P.; Fricker, M. D.; Yumiki, K.; Kobayashi, R.; Nakagaki, T., Rules for biologically inspired adaptive network design, Science, 327, 5964, 439-442 (2010) · Zbl 1226.90021 |
| [34] | Martens, E. A.; Klemm, K., Transitions from trees to cycles in adaptive flow networks, Front. Phys., 5, 62 (2017) |
| [35] | Antoniades, D.; Dovrolis, C., Co-evolutionary dynamics in social networks: A case study of twitter, Comput. Soc. Netw., 2, 1, 1-21 (2015) |
| [36] | Baumann, F.; Lorenz-Spreen, P.; Sokolov, I. M.; Starnini, M., Modeling echo chambers and polarization dynamics in social networks, Phys. Rev. Lett., 124, 4, Article 048301 pp. (2020) |
| [37] | Horstmeyer, L.; Kuehn, C., Adaptive voter model on simplicial complexes, Phys. Rev. E, 101, 2, Article 022305 pp. (2020) |
| [38] | Rajapakse, I.; Groudine, M.; Mesbahi, M., Dynamics and control of state-dependent networks for probing genomic organization, Proc. Natl. Acad. Sci. USA, 108, 42, 17257-17262 (2011) · Zbl 1256.93074 |
| [39] | Morales, G. B.; Mirasso, C. R.; Soriano, M. C., Unveiling the role of plasticity rules in reservoir computing, Neurocomputing, 461, 705-715 (2021) |
| [40] | Liu, Y. Y.; Barabási, A. L., Control principles of complex systems, Rev. Modern Phys., 88, Article 035006 pp. (2016) |
| [41] | Berner, R.; Yanchuk, S.; Schöll, E., What adaptive neuronal networks teach us about power grids, Phys. Rev. E, 103, Article 042315 pp. (2021) |
| [42] | Gutiérrez, R.; Amann, A.; Assenza, S.; Gómez-Gardeñes, J.; Latora, V.; Boccaletti, S., Emerging meso- and macroscales from synchronization of adaptive networks, Phys. Rev. Lett., 107, 23, Article 234103 pp. (2011) |
| [43] | Zhang, X.; Boccaletti, S.; Guan, S.; Liu, Z., Explosive synchronization in adaptive and multilayer networks, Phys. Rev. Lett., 114, 3, Article 038701 pp. (2015) |
| [44] | Maslennikov, O. V.; Nekorkin, V. I., Adaptive dynamical networks, Phys.-Usp., 60, 7, 694-704 (2017) |
| [45] | Kasatkin, D. V.; Yanchuk, S.; Schöll, E.; Nekorkin, V. I., Self-organized emergence of multilayer structure and chimera states in dynamical networks with adaptive couplings, Phys. Rev. E, 96, 6, 62211 (2017) |
| [46] | Madadi Asl, M.; Valizadeh, A.; Tass, P. A., Dendritic and axonal propagation delays may shape neuronal networks with plastic synapses, Front. Physiol., 9, 1849 (2018) |
| [47] | Kasatkin, D. V.; Nekorkin, V. I., Synchronization of chimera states in a multiplex system of phase oscillators with adaptive couplings, Chaos, 28, 93115 (2018) · Zbl 1397.34082 |
| [48] | Berner, R.; Schöll, E.; Yanchuk, S., Multiclusters in networks of adaptively coupled phase oscillators, SIAM J. Appl. Dyn. Syst., 18, 4, 2227-2266 (2019) · Zbl 1540.34101 |
| [49] | Feketa, P.; Schaum, A.; Meurer, T., Synchronization and multi-cluster capabilities of oscillatory networks with adaptive coupling, IEEE Trans. Automat. Control, 66, 7, 3084-3096 (2020) · Zbl 1467.93131 |
| [50] | Berner, R.; Vock, S.; Schöll, E.; Yanchuk, S., Desynchronization transitions in adaptive networks, Phys. Rev. Lett., 126, 2, Article 028301 pp. (2021) |
| [51] | Popovych, O. V.; Xenakis, M. N.; Tass, P. A., The spacing principle for unlearning abnormal neuronal synchrony, PLoS One, 10, 2, Article e0117205 pp. (2015) |
| [52] | Chakravartula, S.; Indic, P.; Sundaram, B.; Killingback, T., Emergence of local synchronization in neuronal networks with adaptive couplings, PLoS One, 12, 6, Article e0178975 pp. (2017) |
| [53] | Röhr, V.; Berner, R.; Lameu, E. L.; Popovych, O. V.; Yanchuk, S., Frequency cluster formation and slow oscillations in neural populations with plasticity, PLoS One, 14, 11, Article e0225094 pp. (2019) |
| [54] | Godsil, C.; Royle, G., Algebraic Graph Theory (2001), Springer-Verlag New York · Zbl 0968.05002 |
| [55] | Costa, L.d. F.; Rodrigues, F. A.; Travieso, G.; Villas Boas, P. R., Characterization of complex networks: A survey of measurements, Adv. Phys., 56, 1, 167-242 (2007) |
| [56] | Newman, M. E.J., Networks: An Introduction (2010), Oxford University Press Inc.: Oxford University Press Inc. New York · Zbl 1195.94003 |
| [57] | Kouvaris, N. E.; Isele, T. M.; Mikhailov, A. S.; Schöll, E., Propagation failure of excitation waves on trees and random networks, Europhys. Lett., 106, 68001 (2014) |
| [58] | Isele, T. M.; Schöll, E., Effect of small-world topology on wave propagation on networks of excitable elements, New J. Phys., 17, Article 023058 pp. (2015) · Zbl 1453.92041 |
| [59] | Isele, T. M.; Hartung, B.; Hövel, P.; Schöll, E., Excitation waves on a minimal small-world model, Eur. Phys. J. B, 88, 4, 104 (2015) |
| [60] | Mulas, R.; Kuehn, C.; Jost, J., Coupled dynamics on hypergraphs: Master stability of steady states and synchronization, Phys. Rev. E, 101, 6, 62313 (2020) |
| [61] | Bianconi, G., Higher-Order Networks (2021), Cambridge University Press · Zbl 1494.82002 |
| [62] | Gambuzza, L. V.; Di Patti, F.; Gallo, L.; Lepri, S.; Romance, M.; Criado, R.; Frasca, M.; Latora, V.; Boccaletti, S., Stability of synchronization in simplicial complexes, Nature Commun., 12, 1255 (2021) |
| [63] | Battiston, F.; Petri, G., Higher-Order Systems (2022), Springer Cham · Zbl 1495.93003 |
| [64] | Hale, J. K.; Lunel, S. M.V., Introduction To Functional Differential Equations, Vol. 99 (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0787.34002 |
| [65] | Yanchuk, S.; Giacomelli, G., Spatio-temporal phenomena in complex systems with time delays, J. Phys. A, 50, 10, Article 103001 pp. (2017) · Zbl 1375.37111 |
| [66] | Gros, C., Complex and Adaptive Dynamical Systems: A Primer (2008), Springer Verlag: Springer Verlag Berlin Heidelberg · Zbl 1146.37002 |
| [67] | Bar-Joseph, I., Spatial and temporal studies of a gated electron gas, invited talk, HCIS-11, Kyoto 1999 (1999) |
| [68] | Albert, R.; Barabási, A. L., Statistical mechanics of complex networks, Rev. Modern Phys., 74, 47-97 (2002) · Zbl 1205.82086 |
| [69] | Jackson, M. O.; Watts, A., The evolution of social and economic networks, J. Econ. Theory, 106, 2, 265-295 (2002) · Zbl 1099.91543 |
| [70] | Koelle, K.; Kamradt, M.; Pascual, M., Understanding the dynamics of rapidly evolving pathogens through modeling the tempo of antigenic change: Influenza as a case study, Epidemics, 1, 2, 129-137 (2009) |
| [71] | Scholtes, I.; Wider, N.; Pfitzner, R.; Garas, A.; Tessone, C. J.; Schweitzer, F., Causality-driven slow-down and speed-up of diffusion in non-markovian temporal networks, Nature Commun., 5, 1, 5024 (2014) |
| [72] | Masuda, N.; Lambiotte, R., A Guide to Temporal Networks (2016), World Scientific · Zbl 1376.60001 |
| [73] | Holme, P.; Saramäki, J., Temporal Network Theory, Vol. 2 (2019), Springer · Zbl 1429.90001 |
| [74] | Ghosh, D.; Frasca, M.; Rizzo, A.; Majhi, S.; Rakshit, S.; Alfaro-Bittner, K.; Boccaletti, S., The synchronized dynamics of time-varying networks, Phys. Rep., 949, 1-63 (2022) · Zbl 1503.93025 |
| [75] | Tsodyks, M.; Pawelzik, K.; Markram, H., Neural networks with dynamic synapses, Neural Comput., 10, 4, 821-835 (1998) |
| [76] | Mongillo, G.; Barak, O.; Tsodyks, M., Synaptic theory of working memory, Science, 319, 5869, 1543-1546 (2008) |
| [77] | Taher, H.; Torcini, A.; Olmi, S., Exact neural mass model for synaptic-based working memory, PLOS Comput. Biol., 16, 12, Article e1008533 pp. (2020) |
| [78] | Schmutz, V.; Gerstner, W.; Schwalger, T., Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity, J. Math. Neurosci., 10, 5 (2020) · Zbl 1443.92050 |
| [79] | Touboul, J.; Brette, R., Dynamics and bifurcations of the adaptive exponential integrate-and-fire model, Biol. Cybernet., 99, 4-5, 319-334 (2008) · Zbl 1161.92016 |
| [80] | Naud, R.; Marcille, N.; Clopath, C.; Gerstner, W., Firing patterns in the adaptive exponential integrate-and-fire model, Biol. cybern., 99, 4-5, 335-347 (2008) · Zbl 1161.92012 |
| [81] | Augustin, M.; Baumann, F.; Ladenbauer, J.; Obermayer, K., Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation, PLOS Comput. Biol., 13, Article e1005545 pp. (2017) |
| [82] | Kuramoto, Y., Chemical Oscillations, Waves and Turbulence (1984), Springer-Verlag: Springer-Verlag Berlin · Zbl 0558.76051 |
| [83] | Strogatz, S., From kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators, Physica D, 143, 1-20 (2000) · Zbl 0983.34022 |
| [84] | Acebrón, J. A.; Bonilla, L. L.; Pérez Vicente, C. J.; Ritort, F.; Spigler, R., The kuramoto model: A simple paradigm for synchronization phenomena, Rev. Modern Phys., 77, 1, 137-185 (2005) |
| [85] | Omelchenko, E.; Wolfrum, M.; Omel’chenko, O. E.; Wolfrum, M., Nonuniversal transitions to synchrony in the Sakaguchi-Kuramoto model, Phys. Rev. Lett., 109, 16, Article 164101 pp. (2012) |
| [86] | Pikovsky, A.; Rosenblum, M., Partially integrable dynamics of hierarchical populations of coupled oscillators, Phys. Rev. Lett., 101, 26, Article 264103 pp. (2008) |
| [87] | Winfree, A. T., The Geometry of Biological Time (1980), Springer: Springer New York · Zbl 0464.92001 |
| [88] | Hoppensteadt, F. C.; Izhikevich, E. M., Weakly Connected Neural Networks (1997), Springer: Springer New York · Zbl 0887.92003 |
| [89] | Pikovsky, A.; Rosenblum, M.; Kurths, J., Synchronization: A Universal Concept in Nonlinear Sciences (2001), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0993.37002 |
| [90] | Pietras, B.; Daffertshofer, A., Network dynamics of coupled oscillators and phase reduction techniques, Phys. Rep., 819, 1-105 (2019) |
| [91] | Ashwin, P.; Coombes, S.; Nicks, R., Mathematical frameworks for oscillatory network dynamics in neuroscience, J. Math. Neurosci., 6, 2 (2016) · Zbl 1356.92015 |
| [92] | Klinshov, V. V.; Yanchuk, S.; Stephan, A.; Nekorkin, V. I., Phase response function for oscillators with strong forcing or coupling, Europhys. Lett., 118, 5, 50006 (2017) |
| [93] | Rosenblum, M.; Pikovsky, A., Numerical phase reduction beyond the first order approximation, Chaos, 29, 1, Article 011105 pp. (2019) · Zbl 1406.34076 |
| [94] | Rosenblum, M.; Pikovsky, A., Nonlinear phase coupling functions: a numerical study, Philos. Trans. Royal Soc. A, 377, 2160, Article 20190093 pp. (2019) · Zbl 1462.34064 |
| [95] | Ermentrout, G. B.; Park, Y.; Wilson, D., Recent advances in coupled oscillator theory, Philos. Trans. Royal Soc. A, 377, 2160, Article 20190092 pp. (2019) · Zbl 1462.34059 |
| [96] | Gkogkas, M. A.; Kuehn, C.; Xu, C., Mean field limits of co-evolutionary heterogeneous networks (2022), arXiv:2202.01742 |
| [97] | Sakaguchi, H.; Kuramoto, Y., A soluble active rotater model showing phase transitions via mutual entertainment, Prog. Theor. Phys, 76, 3, 576-581 (1986) |
| [98] | Aoki, T.; Aoyagi, T., Self-organized network of phase oscillators coupled by activity-dependent interactions, Phys. Rev. E, 84, Article 066109 pp. (2011) |
| [99] | Ren, Q.; Zhao, J., Adaptive coupling and enhanced synchronization in coupled phase oscillators, Phys. Rev. E, 76, 1, Article 016207 pp. (2007) |
| [100] | Aoki, T.; Aoyagi, T., Co-evolution of phases and connection strengths in a network of phase oscillators, Phys. Rev. Lett., 102, Article 034101 pp. (2009) |
| [101] | Picallo, C. B.; Riecke, H., Adaptive oscillator networks with conserved overall coupling: Sequential firing and near-synchronized states, Phys. Rev. E, 83, 3, Article 036206 pp. (2011) |
| [102] | Timms, L.; English, L. Q., Synchronization in phase-coupled Kuramoto oscillator networks with axonal delay and synaptic plasticity, Phys. Rev. E, 89, 3, 32906 (2014) |
| [103] | Gushchin, A.; Mallada, E.; Tang, A., Synchronization of phase-coupled oscillators with plastic coupling strength, (Information Theory and Applications Workshop (2015)), 291-300 |
| [104] | Kasatkin, D. V.; Nekorkin, V. I., Dynamics of the phase oscillators with plastic couplings, Radiophys. Quantum Electron., 58, 11, 877-891 (2016) |
| [105] | Nekorkin, V. I.; Kasatkin, D. V., Dynamics of a network of phase oscillators with plastic couplings, AIP Conf. Proc., 1738, 1, Article 210010 pp. (2016) |
| [106] | Avalos-Gaytán, V.; Almendral, J. A.; Leyva, I.; Battiston, F.; Nicosia, V.; Latora, V.; Boccaletti, S., Emergent explosive synchronization in adaptive complex networks, Phys. Rev. E, 97, 4, Article 042301 pp. (2018) |
| [107] | Niyogi, R. K.; English, L. Q., Learning-rate-dependent clustering and self-development in a network of coupled phase oscillators, Phys. Rev. E, 80, 6, Article 066213 pp. (2009) |
| [108] | Goriely, A.; Kuhl, E.; Bick, C., Neuronal oscillations on evolving networks: Dynamics, damage, degradation, decline, dementia, and death, Phys. Rev. Lett., 125, 12, Article 128102 pp. (2020) |
| [109] | Alexandersen, C. G.; de Haan, W.; Bick, C.; Goriely, A., A multi-scale model explains oscillatory slowing and neuronal hyperactivity in alzheimer’s disease, J. R. Soc. Interface, 20, 198, Article 20220607 pp. (2023) |
| [110] | Clopath, C.; Büsing, L.; Vasilaki, E.; Gerstner, W., Connectivity reflects coding: a model of voltage-based STDP with homeostasis, Nature Neurosci., 13, 3, 344-352 (2010) |
| [111] | Meissner-Bernard, C.; Tsai, M. C.; Logiaco, L.; Gerstner, W., Dendritic voltage recordings explain paradoxical synaptic plasticity: A modeling study, Front. Synaptic Neurosci., 12, Article 585539 pp. (2020) |
| [112] | Rubinov, M.; Sporns, O.; Van Leeuwen, C.; Breakspear, M., Symbiotic relationship between brain structure and dynamics, BMC Neurosci., 10, 1, 55 (2009) |
| [113] | Virkar, Y. S.; Shew, W. L.; Restrepo, J. G.; Ott, E., Feedback control stabilization of critical dynamics via resource transport on multilayer networks: How glia enable learning dynamics in the brain, Phys. Rev. E, 94, 4, Article 042310 pp. (2016) |
| [114] | Kroma-Wiley, K. A.; Mucha, P. J.; Bassett, D. S., Synchronization of coupled kuramoto oscillators under resource constraints, Phys. Rev. E, 104, Article 014211 pp. (2021) |
| [115] | Franović, I.; Eydam, S.; Yanchuk, S.; Berner, R., Collective activity bursting in networks of excitable systems adaptively coupled to a pool of resources, Front. Netw. Physiol., 2, Article 841829 pp. (2022) |
| [116] | Gerstner, W.; Kistler, W. M.; Naud, R.; Paninski, L., Neuronal Dynamics: From Single Neurons To Networks and Models of Cognition (2014), Cambridge University Press |
| [117] | Froemke, R. C.; Poo, M. M.; Dan, Y., Spike-timing-dependent synaptic plasticity depends on dendritic location, Nature, 434, 7030, 221-225 (2005) |
| [118] | Froemke, R. C.; Letzkus, J. J.; Kampa, B. M.; Hang, G. B.; Stuart, G. J., Dendritic synapse location and neocortical spike-timing-dependent plasticity, Front. Synaptic Neurosci., 2, Article 29 pp. (2010) |
| [119] | Sjöström, P. J.; Häusser, M., A cooperative switch determines the sign of synaptic plasticity in distal dendrites of neocortical pyramidal neurons, Neuron, 51, 2, 227-238 (2006) |
| [120] | Letzkus, J. J.; Kampa, B. M.; Stuart, G. J., Learning rules for spike timing-dependent plasticity depend on dendritic synapse location, J. Neurosci., 26, 41, 10420-10429 (2006) |
| [121] | Maistrenko, Y.; Lysyansky, B.; Hauptmann, C.; Burylko, O.; Tass, P. A., Multistability in the kuramoto model with synaptic plasticity, Phys. Rev. E, 75, 6, Article 066207 pp. (2007) |
| [122] | Popovych, O. V.; Yanchuk, S.; Tass, P. A., Self-organized noise resistance of oscillatory neural networks with spike timing-dependent plasticity, Sci. Rep., 3, 2926 (2013) |
| [123] | Thiele, M.; Berner, R.; Tass, P. A.; Schöll, E.; Yanchuk, S., Asymmetric adaptivity induces recurrent synchronization in complex networks, Chaos, 33, 2, Article 023123 pp. (2023) · Zbl 07881250 |
| [124] | Butz, M.; Wörgötter, F.; van Ooyen, A., Activity-dependent structural plasticity, Brain Res. Rev., 60, 2, 287-305 (2009) |
| [125] | Butz, M.; van Ooyen, A., A simple rule for dendritic spine and axonal bouton formation can account for cortical reorganization after focal retinal lesions, PLoS Comput. Biol., 9, 10, Article e1003259 pp. (2013) |
| [126] | Van Ooyen, A.; Butz-Ostendorf, M., The Rewiring Brain : A Computational Approach To Structural Plasticity in the Adult Brain (2017), Academic Press |
| [127] | Nowke, C.; Diaz-Pier, S.; Weyers, B.; Hentschel, B.; Morrison, A.; Kuhlen, T. W.; Peyser, A., Toward rigorous parameterization of underconstrained neural network models through interactive visualization and steering of connectivity generation, Front. Neuroinform., 12, 32 (2018) |
| [128] | Diaz-Pier, S.; Naveau, M.; Butz-Ostendorf, M.; Morrison, A., Automatic generation of connectivity for large-scale neuronal network models through structural plasticity, Front. Neuroanat., 10, MAY, 57 (2016) |
| [129] | Manos, T.; Diaz Pier, S.; Tass, P. A., Long-term desynchronization by coordinated reset stimulation in a neural network model with synaptic and structural plasticity, Front. Physiol., 12, Article 716556 pp. (2021) |
| [130] | Ivanov, P. C., The new field of network physiology: Building the human physiolome, Front. Netw. Physiol., 1, Article 711778 pp. (2021) |
| [131] | Schöll, E.; Sawicki, J.; Berner, R.; Ivanov, P. C., Editorial: Adaptive networks in functional modeling of physiological systems, Front. Netw. Physiol., 2, Article 996784 pp. (2022) |
| [132] | Schuurman, A. R.; Sloot, P.; Wiersinga, W. J.; van der Poll, T., Embracing complexity in sepsis, Critical Care, 27, 1, 1-8 (2023) |
| [133] | Morán, G. A.G.; Parra-Medina, R.; Cardona, A. G.; Quintero-Ronderos, P.; Rodríguez, É. G., Cytokines, chemokines and growth factors, (Anaya, J. M.; Shoenfeld, Y.; Rojas-Villarraga, A.; Levy, R. A.; Cervera, R., Autoimmunity: From Bench To Bedside (2013), El Rosario University Press: El Rosario University Press Bogota, Colombia), 133-168, (Chapter 9) |
| [134] | Altan-Bonnet, G.; Mukherjee, R., Cytokine-mediated communication: a quantitative appraisal of immune complexity, Nat. Rev. Immunol., 19, 4, 205-217 (2019) |
| [135] | Fleischmann, C.; Thomas-Rueddel, D. O.; Hartmann, M.; Hartog, C. S.; Welte, T.; Heublein, S.; Dennler, U.; Reinhart, K., Hospital incidence and mortality rates of sepsis: an analysis of hospital episode (DRG) statistics in Germany from 2007 to 2013, Dtsch. Arztebl. Int., 113, 10, 159 (2016) |
| [136] | LeCun, Y.; Bengio, Y.; Hinton, G., Deep learning, Nature, 521, 436 (2015) |
| [137] | Goodfellow, I.; Bengio, Y.; Courville, A., Deep Learning (2016), MIT Press: MIT Press Cambridge, Massachusetts, London, England · Zbl 1373.68009 |
| [138] | Rumelhart, D.; Hinton, G. E.; Williams, R. J., Learning representations by back-propagating errors, Nature, 323, 533-536 (1986) · Zbl 1369.68284 |
| [139] | H. Jaeger, The Echo State Approach To Analysing and Training Recurrent Neural Networks, German National Research Center for Information Technology GMD Technical Report 148, 2001. |
| [140] | Maass, W.; Natschläger, T.; Markram, H., Real-time computing without stable states: A new framework for neural computation based on perturbations, Neural Comput., 14, 11, 2531-2560 (2002) · Zbl 1057.68618 |
| [141] | Babinec, Å.; Pospíchal, J., (Improving the Prediction Accuracy of Echo State Neural Networks By Anti-Oja’s Learning. Improving the Prediction Accuracy of Echo State Neural Networks By Anti-Oja’s Learning, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 4668 LNCS (PART 1) (2007)), 19-28 |
| [142] | Triesch, J., A gradient rule for the plasticity of a neuron’s intrinsic excitability, (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3696 LNCS (2005), Springer: Springer Berlin, Heidelberg), 65-70 |
| [143] | Schrauwen, B.; Wardermann, M.; Verstraeten, D.; Steil, J. J.; Stroobandt, D., Improving reservoirs using intrinsic plasticity, Neurocomputing, 71, 7-9, 1159-1171 (2008) |
| [144] | Steil, J. J., Online reservoir adaptation by intrinsic plasticity for backpropagation-decorrelation and echo state learning, Neural Netw., 20, 3, 353-364 (2007) · Zbl 1132.68594 |
| [145] | Wang, X.; Jin, Y.; Hao, K., Echo state networks regulated by local intrinsic plasticity rules for regression, Neurocomputing, 351, 111-122 (2019) |
| [146] | Yusoff, M. H.; Chrol-Cannon, J.; Jin, Y., Modeling neural plasticity in echo state networks for classification and regression, Inform. Sci., 364-365, 184-196 (2016) |
| [147] | Andreev, A. V.; Badarin, A. A.; Maximenko, V. A.; Hramov, A. E., Forecasting macroscopic dynamics in adaptive Kuramoto network using reservoir computing, Chaos, 32, 10, Article 103126 pp. (2022) · Zbl 07879596 |
| [148] | Yakubovich, V. A., Theory of adaptive systems, Sov. Phys. - Doklady, 13, 9, 852-855 (1969) · Zbl 0181.47604 |
| [149] | Annaswamy, A. M.; Fradkov, A. L., A historical perspective of adaptive control and learning, Annu. Rev. Control., 52, 18-41 (2021) |
| [150] | Mesbahi, M., On state-dependent dynamic graphs and their controllability properties, IEEE Trans. Automat. Control, 50, 3, 387-392 (2005) · Zbl 1365.93045 |
| [151] | Xuan, Q.; Du, F.; Dong, H.; Yu, L.; Chen, G., Structural control of reaction-diffusion networks, Phys. Rev. E, 84, Article 036101 pp. (2011) |
| [152] | Chen, M.; Shang, Y.; Zou, Y.; Kurths, J., Synchronization in the kuramoto model: A dynamical gradient network approach, Phys. Rev. E, 77, Article 027101 pp. (2008) |
| [153] | DeLellis, P.; di Bernardo, M.; Gorochowski, T. E.; Russo, G., Synchronization and control of complex networks via contraction, adaptation and evolution, IEEE Trans. Circ. Syst., 10, 3, 64-82 (2010) |
| [154] | Zhou, C.; Kurths, J., Dynamical weights and enhanced synchronization in adaptive complex networks, Phys. Rev. Lett., 96, 16, Article 164102 pp. (2006) |
| [155] | DeLellis, P.; di Bernardo, M.; Garofalo, F., Synchronization of complex networks through local adaptive coupling, Chaos, 18, 3, Article 037110 pp. (2008) · Zbl 1309.34090 |
| [156] | Sorrentino, F.; Ott, E., Adaptive synchronization of dynamics on evolving complex networks, Phys. Rev. Lett., 100, 11, Article 114101 pp. (2008) |
| [157] | Sorrentino, F.; Barlev, G.; Cohen, A. B.; Ott, E., The stability of adaptive synchronization of chaotic systems, Chaos, 20, 1, Article 013103 pp. (2010) · Zbl 1311.34098 |
| [158] | Ravoori, B.; Cohen, A. B.; Setty, A. V.; Sorrentino, F.; Murphy, T. E.; Ott, E.; Roy, R., Adaptive synchronization of coupled chaotic oscillators, Phys. Rev. E, 80, Article 056205 pp. (2009) |
| [159] | DeLellis, P.; di Bernardo, M.; Russo, G., On quad, lipschitz, and contracting vector fields for consensus and synchronization of networks, IEEE Trans. Circ. Syst. I Regul. Pap., 58, 3, 576-583 (2011) · Zbl 1468.34077 |
| [160] | DeLellis, P.; di Bernardo, M.; Garofalo, F., Novel decentralized adaptive strategies for the synchronization of complex networks, Automatica, 45, 5, 1312-1318 (2009) · Zbl 1162.93361 |
| [161] | DeLellis, P.; di Bernardo, M.; Sorrentino, F.; Tierno, A., Adaptive synchronization of complex networks, Int. J. Comput. Math., 85, 8, 1189-1218 (2008) · Zbl 1142.93361 |
| [162] | DeLellis, P.; di Bernardo, M.; Garofalo, F., Decentralized adaptive control for synchronization and consensus of complex networks, (Chiuso, A.; Fortuna, L.; Frasca, M.; Rizzo, A.; Schenato, L.; Zampieri, S., Modelling, Estimation and Control of Networked Complex Systems (2009), Springer Berlin Heidelberg), 27-42 |
| [163] | Yu, W.; DeLellis, P.; Chen, G.; di Bernardo, M.; Kurths, J., Distributed adaptive control of synchronization in complex networks, IEEE Trans. Automat. Control, 57, 8, 2153-2158 (2012) · Zbl 1369.93321 |
| [164] | DeLellis, P.; di Bernardo, M.; Garofalo, F.; Porfiri, M., Evolution of complex networks via edge snapping, IEEE Trans. Circuits Syst. I, 57, 8, 2132-2143 (2010) · Zbl 1468.93093 |
| [165] | Fradkov, A. L., Cybernetical Physics: From Control of Chaos To Quantum Control (2007), Springer: Springer Heidelberg, Germany · Zbl 1117.81002 |
| [166] | Lehnert, J.; Hövel, P.; Selivanov, A. A.; Fradkov, A. L.; Schöll, E., Controlling cluster synchronization by adapting the topology, Phys. Rev. E, 90, 4, Article 042914 pp. (2014) |
| [167] | Lehnert, J.; Selivanov, A.; Hövel, P.; Fradkov, A. L.; Schöll, E., Adaptive control of cluster synchronization in delay-coupled networks, IPACS electronic libraryphyscon 2015 in Istanbul (2015), http://lib.physcon.ru |
| [168] | Lehnert, J., Controlling Synchronization Patterns in Complex Networks (2016), Springer: Springer Heidelberg, (Springer theses) |
| [169] | Bergen, A. R.; Hill, D. J., A structure preserving model for power system stability analysis, IEEE T. Power Apparatus and Syst., 100, 1, 25-35 (1981) |
| [170] | Salam, F. M.A.; Marsden, J. E.; Varaiya, P. P., Arnold diffusion in the swing equations of a power system, IEEE Trans. Circuits Syst., 31, 8, 673-688 (1984) · Zbl 0561.58013 |
| [171] | Sauer, P. W.; Pai, M. A., Power System Dynamics and Stability (1998), Prentice hall: Prentice hall Upper Saddle River, NJ |
| [172] | Filatrella, G.; Nielsen, A. H.; Pedersen, N. F., Analysis of a power grid using a kuramoto-like model, Eur. Phys. J. B, 61, 4, 485-491 (2008) |
| [173] | Schiffer, J.; Zonetti, D.; Ortega, R.; Stankovic, A. M., A survey on modeling of microgrids-from fundamental physics to phasors and voltage sources, Automatica, 74, 135-150 (2016) · Zbl 1348.93038 |
| [174] | Dörfler, F.; Chertkov, M.; Bullo, F., Synchronization in complex oscillator networks and smart grids, Proc. Natl. Acad. Sci. USA, 110, 6, 2005-2010 (2013) · Zbl 1292.94185 |
| [175] | Weckesser, T.; Johannsson, H.; Ostergaard, J., Impact of model detail of synchronous machines on real-time transient stability assessment, (2013 IREP Symposium Bulk Power System Dynamics and Control - IX Optimization, Security and Control of the Emerging Power Grid (2013), IEEE: IEEE Piscataway, NJ, USA) |
| [176] | Nishikawa, T.; Motter, A. E., Comparative analysis of existing models for power-grid synchronization, New J. Phys., 17, 1, Article 015012 pp. (2015) · Zbl 1452.91229 |
| [177] | Auer, S.; Kleis, K.; Schultz, P.; Kurths, J.; Hellmann, F., The impact of model detail on power grid resilience measures, Eur. Phys. J. Spec. Top., 225, 3, 609-625 (2016) |
| [178] | Dörfler, F.; Bullo, F., Synchronization and transient stability in power networks and nonuniform kuramoto oscillators, SIAM J. Control Optim., 50, 3, 1616-1642 (2012) · Zbl 1264.34105 |
| [179] | Rohden, M.; Sorge, A.; Timme, M.; Witthaut, D., Self-organized synchronization in decentralized power grids, Phys. Rev. Lett., 109, Article 064101 pp. (2012) |
| [180] | Cornelius, S. P.; Kath, W. L.; Motter, A. E., Realistic control of network dynamics, Nature Commun., 4, 1942 (2013) |
| [181] | Motter, A. E.; Myers, S. A.; Anghel, M.; Nishikawa, T., Spontaneous synchrony in power-grid networks, Nat. Phys., 9, 191-197 (2013) |
| [182] | Dörfler, F.; Bullo, F., Synchronization in complex networks of phase oscillators: A survey, Automatica, 50, 6, 1539-1564 (2014) · Zbl 1296.93005 |
| [183] | Menck, P. J.; Heitzig, J.; Kurths, J.; Schellnhuber, H. J., How dead ends undermine power grid stability, Nature Commun., 5, 3969 (2014) |
| [184] | Rodrigues, F. A.; Peron, T. K.D. M.; Ji, P.; Kurths, J., The Kuramoto model in complex networks, Phys. Rep., 610, 1-98 (2016) · Zbl 1357.34089 |
| [185] | Witthaut, D.; Rohden, M.; Zhang, X.; Hallerberg, S.; Timme, M., Critical links and nonlocal rerouting in complex supply networks, Phys. Rev. Lett., 116, Article 138701 pp. (2016) |
| [186] | Auer, S.; Hellmann, F.; Krause, M.; Kurths, J., Stability of synchrony against local intermittent fluctuations in tree-like power grids, Chaos, 27, 12, Article 127003 pp. (2017) |
| [187] | Mehrmann, V.; Morandin, R.; Olmi, S.; Schöll, E., Qualitative stability and synchronicity analysis of power network models in port-Hamiltonian form, Chaos, 28, 10, Article 101102 pp. (2018) · Zbl 1442.37113 |
| [188] | Schäfer, B.; Beck, C.; Aihara, K.; Witthaut, D.; Timme, M., Non-Gaussian power grid frequency fluctuations characterized by levy-stable laws and superstatistics, Nat. Energy, 3, 119 (2018) |
| [189] | Taher, H.; Olmi, S.; Schöll, E., Enhancing power grid synchronization and stability through time delayed feedback control, Phys. Rev. E, 100, 6, Article 062306 pp. (2019) |
| [190] | Hellmann, F.; Schultz, P.; Jaros, P.; Levchenko, R.; Kapitaniak, T.; Kurths, J.; Maistrenko, Y., Network-induced multistability through lossy coupling and exotic solitary states, Nature Commun., 11, 592 (2020) |
| [191] | Kuehn, C.; Throm, S., Power network dynamics on graphons, SIAM J. Appl. Math., 79, 4, 1271-1292 (2019) · Zbl 1428.37026 |
| [192] | Molnar, F.; Nishikawa, T.; Motter, A. E., Network experiment demonstrates converse symmetry breaking, Nat. Phys., 16, 351-356 (2020) |
| [193] | Totz, C. H.; Olmi, S.; Schöll, E., Control of synchronization in two-layer power grids, Phys. Rev. E, 102, Article 022311 pp. (2020) |
| [194] | Zhang, X.; Ma, C.; Timme, M., Vulnerability in dynamically driven oscillatory networks and power grids, Chaos, 30, 6, Article 063111 pp. (2020) · Zbl 1440.34053 |
| [195] | Groß, D.; Colombino, M.; Brouillon, J. S.; Dorfler, F., The effect of transmission-line dynamics on grid-forming dispatchable virtual oscillator control, IEEE Trans. Control Netw. Syst., 6, 3, 1148-1160 (2019) · Zbl 1515.93088 |
| [196] | Jaros, P.; Brezetsky, S.; Levchenko, R.; Dudkowski, D.; Kapitaniak, T.; Maistrenko, Y., Solitary states for coupled oscillators with inertia, Chaos, 28, Article 011103 pp. (2018) · Zbl 1390.34136 |
| [197] | Berner, R.; Polanska, A.; Schöll, E.; Yanchuk, S., Solitary states in adaptive nonlocal oscillator networks, Eur. Phys. J. Spec. Top., 229, 12-13, 2183-2203 (2020) |
| [198] | Belykh, I. V.; Brister, B. N.; Belykh, V. N., Bistability of patterns of synchrony in Kuramoto oscillators with inertia, Chaos, 26, Article 094822 pp. (2016) · Zbl 1382.34037 |
| [199] | Berner, R.; Fialkowski, J.; Kasatkin, D. V.; Nekorkin, V. I.; Yanchuk, S.; Schöll, E., Hierarchical frequency clusters in adaptive networks of phase oscillators, Chaos, 29, 10, Article 103134 pp. (2019) · Zbl 1425.34062 |
| [200] | Tumash, L.; Olmi, S.; Schöll, E., Stability and control of power grids with diluted network topology, Chaos, 29, Article 123105 pp. (2019) · Zbl 1429.34059 |
| [201] | Olmi, S., Chimera states in coupled Kuramoto oscillators with inertia, Chaos, 25, Article 123125 pp. (2015) · Zbl 1374.34117 |
| [202] | Olmi, S.; Navas, A.; Boccaletti, S.; Torcini, A., Hysteretic transitions in the Kuramoto model with inertia, Phys. Rev. E, 90, 4, Article 042905 pp. (2014) |
| [203] | Barré, J.; Métivier, D., Bifurcations and singularities for coupled oscillators with inertia and frustration, Phys. Rev. Lett., 117, 21, Article 214102 pp. (2016) |
| [204] | Tumash, L.; Olmi, S.; Schöll, E., Effect of disorder and noise in shaping the dynamics of power grids, Europhys. Lett., 123, 20001 (2018) |
| [205] | Yang, Y.; Motter, A. E., Cascading failures as continuous phase-space transitions, Phys. Rev. Lett., 199, Article 248302 pp. (2017) |
| [206] | Schmietendorf, K.; Peinke, J.; Friedrich, R.; Kamps, O., Self-organized synchronization and voltage stability in networks of synchronous machines, Eur. Phys. J. Spec. Top., 223, 2577 (2014) |
| [207] | Ciszak, M.; Marino, F.; Torcini, A.; Olmi, S., Emergent excitability in populations of nonexcitable units, Phys. Rev. E, 102, 5, Article 050201 pp. (2020), (R) |
| [208] | Acebrón, J. A.; Spigler, R., Adaptive frequency model for phase-frequency synchronization in large populations of globally coupled nonlinear oscillators, Phys. Rev. Lett., 81, 2229, 2229 (1998) |
| [209] | Taylor, D.; Ott, E.; Restrepo, J. G., Spontaneous synchronization of coupled oscillator systems with frequency adaptation, Phys. Rev. E, 81, 4, Article 046214 pp. (2010) |
| [210] | Skardal, P. S.; Taylor, D.; Restrepo, J. G., Complex macroscopic behavior in systems of phase oscillators with adaptive coupling, Physica D, 267, 27-35 (2013) · Zbl 1292.34071 |
| [211] | Schäfer, B.; Witthaut, D.; Timme, M.; Latora, V., Dynamically induced cascading failures in power grids, Nature Commun., 9, 1975 (2018) |
| [212] | Brezetsky, S.; Jaros, P.; Levchenko, R.; Kapitaniak, T.; Maistrenko, Y., Chimera complexity, Phys. Rev. E, 103, Article L050204 pp. (2021) |
| [213] | Hennig, M. H., Theoretical models of synaptic short term plasticity, Front. Comput. Neurosci., 7, 45 (2013) |
| [214] | Abraham, W. C.; Bear, M. F., Metaplasticity: the plasticity of synaptic plasticity, Trends Neurosci., 19, 4, 126-130 (1996) |
| [215] | Abraham, W. C., Metaplasticity: tuning synapses and networks for plasticity, Nat. Rev. Neurosci., 9, 387 (2008) |
| [216] | Ren, W.; Beard, R. W.; Atkins, E. M., A survey of consensus problems in multi-agent coordination, (Proceedings of the 2005, American Control Conference (2005), IEEE) |
| [217] | Yu, W.; Chen, G.; Cao, M.; Kurths, J., Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics, IEEE Trans. Sys. Man Cyb., 40, 3, 881-891 (2010) |
| [218] | Paczuski, M.; Bassler, K. E.; Corral, A., Self-organized networks of competing boolean agents, Phys. Rev. Lett., 84, 14, 3185-3188 (2000) |
| [219] | Kauffman, S., Homeostasis and differentiation in random genetic control networks, Nature, 224, 5215, 177-178 (1969) |
| [220] | Bornholdt, S.; Rohlf, T., Topological evolution of dynamical networks: global criticality from local dynamics, Phys. Rev. Lett., 84, 26, 6114-6117 (2000) |
| [221] | Jiang, C.; Chen, Y.; Liu, K. J.R., Distributed adaptive networks: A graphical evolutionary game-theoretic view, IEEE Trans. Signal Process., 61, 22, 5675-5688 (2013) · Zbl 1393.94283 |
| [222] | Farajtabar, M.; Wang, Y.; Gomez Rodriguez, M.; Li, S.; Zha, H.; Song, L., Coevolve: A joint point process model for information diffusion and network co-evolution, (Cortes, C.; Lawrence, N.; Lee, D.; Sugiyama, M.; Garnett, R., Advances in Neural Information Processing Systems, Vol .28 (2015), Curran Associates, Inc.), URL https://proceedings.neurips.cc/paper/2015/file/52292e0c763fd027c6eba6b8f494d2eb-Paper.pdf |
| [223] | Zimmermann, M. G.; Eguíluz, V. M.; San Miguel, M.; Spadaro, A., Cooperation in an adaptive network, Adv. Complex Syst., 03, 01n04, 283-297 (2011) |
| [224] | Skyrms, B.; Pemantle, R., A dynamic model of social network formation, Proc. Natl. Acad. Sci., 97, 16, 9340-9346 (2000) · Zbl 0984.91013 |
| [225] | Ebel, H.; Bornholdt, S., Evolutionary games and the emergence of complex networks (2002), arXiv:cond-mat/0211666 |
| [226] | Goyal, S.; Vega-Redondo, F., Network formation and social coordination, Games Econom. Behav., 50, 2, 178-207 (2005) · Zbl 1109.91323 |
| [227] | Gräser, O.; Xu, C.; Hui, P. M., Disconnected-connected network transitions and phase separation driven by co-evolving dynamics, Europhys. Lett., 87, 3, 38003 (2009) |
| [228] | Szolnoki, A.; Perc, M., Emergence of multilevel selection in the prisoner’s dilemma game on coevolving random networks, New J. Phys., 11, 9, Article 093033 pp. (2009) |
| [229] | Van Segbroeck, S.; Santos, F. C.; Lenaerts, T.; Pacheco, J. M., Reacting differently to adverse ties promotes cooperation in social networks, Phys. Rev. Lett., 102, 5, Article 058105 pp. (2009) |
| [230] | Zhang, W.; Li, Y. S.; Du, P.; Xu, C.; Hui, P. M., Phase transitions in a coevolving snowdrift game with costly rewiring, Phys. Rev. E, 90, 5, Article 052819 pp. (2014) |
| [231] | Pacheco, J. M.; Traulsen, A.; Nowak, M. A., Coevolution of strategy and structure in complex networks with dynamical linking, Phys. Rev. Lett., 97, 25, Article 258103 pp. (2006) |
| [232] | Hojman, D. A.; Szeidl, A., Endogenous networks, social games, and evolution, Games Econom. Behav., 55, 1, 112-130 (2006) · Zbl 1138.91339 |
| [233] | Biely, C.; Dragosits, K.; Thurner, S., The prisoner’s dilemma on co-evolving networks under perfect rationality, Physica D, 228, 1, 40-48 (2007) · Zbl 1200.91034 |
| [234] | Poncela, J.; Gómez-Gardeñes, J.; Floría, L. M.; Sánchez, A.; Moreno, Y., Complex cooperative networks from evolutionary preferential attachment, PLoS One, 3, 6, Article e2449 pp. (2008) |
| [235] | Perc, M.; Szolnoki, A., Coevolutionary games-a mini review, Biosystems, 99, 2, 109-125 (2010) |
| [236] | Santos, F. C.; Pacheco, J. M.; Lenaerts, T., Cooperation prevails when individuals adjust their social ties, PLoS Comput. Biol., 2, 10, Article e140 pp. (2006) |
| [237] | Rand, D. G.; Arbesman, S.; Christakis, N. A., Dynamic social networks promote cooperation in experiments with humans, Proc. Natl. Acad. Sci., 108, 48, 19193-19198 (2011) |
| [238] | Zschaler, G.; Traulsen, A.; Gross, T., A homoclinic route to asymptotic full cooperation in adaptive networks and its failure, New J. Phys., 12, Article 093015 pp. (2010) |
| [239] | Demirel, G.; Prizak, R.; Reddy, P. N.; Gross, T., Cyclic dominance in adaptive networks, Eur. Phys. J. B, 84, 4, 541-548 (2011) |
| [240] | Do, A.-L.; Rudolf, L.; Gross, T., Patterns of cooperation: fairness and coordination in networks of interacting agents, New J. Phys., 12, 6, Article 063023 pp. (2010) · Zbl 1382.91014 |
| [241] | Mogielski, K.; Płatkowski, T., A mechanism of dynamical interactions for two-person social dilemmas, J. Theoret. Biol., 260, 1, 145-150 (2009) · Zbl 1402.91084 |
| [242] | Holme, P.; Ghoshal, G., Dynamics of networking agents competing for high centrality and low degree, Phys. Rev. Lett., 96, 9, Article 098701 pp. (2006) |
| [243] | Deng, L. L.; Wang, C.; Tang, W. S.; Zhou, G. G.; Cai, J. H., A network growth model based on the evolutionary ultimatum game, J. Stat. Mech. Theory Exp., 2012, 11, Article P11013 pp. (2012) |
| [244] | Yuan, Y.; Alabdulkareem, A.; Pentland, A. S., An interpretable approach for social network formation among heterogeneous agents, Nature Commun., 9, 1, 4704 (2018) |
| [245] | Fahimipour, A. K.; Zeng, F.; Homer, M.; Traulsen, A.; Levin, S. A.; Gross, T., Sharp thresholds limit the benefit of defector avoidance in cooperation on networks, Proc. Natl. Acad. Sci., 119, 33, Article e2120120119 pp. (2022) |
| [246] | Zschaler, G.; Böhme, G.; Seissinger, M.; Huepe, C.; Gross, T., Early fragmentation in the adaptive voter model on directed networks, Phys. Rev. E, 85, 4, Article 046107 pp. (2012) |
| [247] | French, J. R.P., A formal theory of social power., Psychol. Rev., 63, 3, 181-194 (1956) |
| [248] | Harary, F., A criterion for unanimity in french’s theory of social power, (Cartwright, D., Studies in Social Power (1959), Michigan Univrsity: Michigan Univrsity Ann Arbor), 168-182 |
| [249] | Deffuant, G.; Neau, D.; Amblard, F.; Weisbuch, G., Mixing beliefs among interacting agents, Adv. Complex Syst., 03, 01n04, 87-98 (2000) |
| [250] | Sznajd-Weron, K.; Sznajd, J., Opinion evolution in closed community, Internat. J. Modern Phys. C, 11, 06, 1157-1165 (2001) |
| [251] | Hegselmann, R.; Krause, U., Opinion dynamics and bounded confidence models, analysis, and simulation, J. Artif. Soc. Soc. Simul., 5, 3, 1-33 (2002) |
| [252] | Zanette, D. H.; Gil, S., Opinion spreading and agent segregation on evolving networks, Physica D, 224, 1-2, 156-165 (2006) · Zbl 1129.90014 |
| [253] | Gil, S.; Zanette, D. H., Coevolution of agents and networks: Opinion spreading and community disconnection, Phys. Lett. A, 356, 2, 89-94 (2006) · Zbl 1160.91404 |
| [254] | Holme, P.; Newman, M., Nonequilibrium phase transition in the coevolution of networks and opinions, Phys. Rev. E, 74, Article 056108 pp. (2006) |
| [255] | Centola, D.; González-Avella, J. C.; Eguíluz, V. M.; San Miguel, M., And the co-evolution of cultural groups, J. Confl. Resolut., 51, 6, 905-929 (2007) |
| [256] | Biely, C.; Hanel, R.; Thurner, S., Socio-economical dynamics as a solvable spin system on co-evolving networks, Eur. Phys. J. B, 67, 3, 285-289 (2008) |
| [257] | Sobkowicz, P., Studies of opinion stability for small dynamic networks with opportunistic agents, Internat. J. Modern Phys. C, 20, 10, 1645-1662 (2009) · Zbl 1187.91166 |
| [258] | Kozma, B.; Barrat, A., Consensus formation on adaptive networks, Phys. Rev. E, 77, 1, Article 016102 pp. (2008) |
| [259] | Nardini, C.; Kozma, B.; Barrat, A., Who’s talking first? Consensus or lack thereof in coevolving opinion formation models, Phys. Rev. Lett., 100, Article 158701 pp. (2008) |
| [260] | Herrera, J. L.; Cosenza, M. G.; Tucci, K.; González-Avella, J. C., General coevolution of topology and dynamics in networks, Europhys. Lett., 95, 5, 58006 (2011) |
| [261] | Durrett, R.; Gleeson, J. P.; Lloyd, A. L.; Mucha, P. J.; Shi, F.; Sivakoff, D.; Socolar, J. E.S.; Varghese, C., Graph fission in an evolving voter model, Proc. Natl. Acad. Sci., 109, 10, 3682-3687 (2012) · Zbl 1256.91042 |
| [262] | Kimura, D.; Hayakawa, Y., Coevolutionary networks with homophily and heterophily, Phys. Rev. E, 78, Article 016103 pp. (2008) |
| [263] | Wiedermann, M.; Donges, J. F.; Heitzig, J.; Lucht, W.; Kurths, J., Macroscopic description of complex adaptive networks coevolving with dynamic node states, Phys. Rev. E, 91, 5, Article 052801 pp. (2015) |
| [264] | Min, B.; Miguel, M. S., Fragmentation transitions in a coevolving nonlinear voter model, Sci. Rep., 7, 1, 12864 (2017) |
| [265] | Vazquez, F.; Eguíluz, V. M.; Miguel, M. S., Generic absorbing transition in coevolution dynamics, Phys. Rev. Lett., 100, 10, Article 108702 pp. (2008) |
| [266] | Demirel, G.; Vazquez, F.; Böhme, G.; Gross, T., Moment-closure approximations for discrete adaptive networks, Physica D, 267, 68-80 (2014) · Zbl 1285.93013 |
| [267] | Silk, H.; Demirel, G.; Homer, M.; Gross, T., Exploring the adaptive voter model dynamics with a mathematical triple jump, New J. Phys., 16, 9, Article 093051 pp. (2014) |
| [268] | Böhme, G.; Gross, T., Analytical calculation of fragmentation transitions in adaptive networks, Phys. Rev. E, 83, Article 035101 pp. (2011) |
| [269] | Rogers, T.; Gross, T., Consensus time and conformity in the adaptive voter model, Phys. Rev. E, 88, 3, Article 030102 pp. (2013) |
| [270] | Carro, A.; Toral, R.; San Miguel, M., The noisy voter model on complex networks, Sci. Rep., 6, 1, 24775 (2016) |
| [271] | Klamser, P. P.; Wiedermann, M.; Donges, J. F.; Donner, R. V., Zealotry effects on opinion dynamics in the adaptive voter model, Phys. Rev. E, 96, 5, Article 052315 pp. (2017) |
| [272] | Raducha, T.; San Miguel, M., Emergence of complex structures from nonlinear interactions and noise in coevolving networks, Sci. Rep., 10, 1, 15660 (2020) |
| [273] | Papanikolaou, N.; Vaccario, G.; Hormann, E.; Lambiotte, R.; Schweitzer, F., Consensus from group interactions: An adaptive voter model on hypergraphs, Phys. Rev. E, 105, 5, Article 054307 pp. (2022) |
| [274] | Diakonova, M.; San Miguel, M.; Eguíluz, V. M., Absorbing and shattered fragmentation transitions in multilayer coevolution, Phys. Rev. E, 89, 6, Article 062818 pp. (2014) |
| [275] | Müller-Hansen, F.; Schlüter, M.; Mäs, M.; Donges, J. F.; Kolb, J. J.; Thonicke, K.; Heitzig, J., Towards representing human behavior and decision making in earth system models – an overview of techniques and approaches, Earth Syst. Dyn., 8, 4, 977-1007 (2017) |
| [276] | Huepe, C.; Zschaler, G.; Do, A.-L.; Gross, T., Adaptive-network models of swarm dynamics, New J. Phys., 13, 7, Article 073022 pp. (2011) |
| [277] | Couzin, I. D.; Ioannou, C. C.; Demirel, G.; Gross, T.; Torney, C. J.; Hartnett, A.; Conradt, L.; Levin, S. A.; Leonard, N. E., Uninformed individuals promote democratic consensus in animal groups, Science, 334, 6062, 1578-1580 (2011) |
| [278] | Chen, L.; Huepe, C.; Gross, T., Adaptive network models of collective decision making in swarming systems, Phys. Rev. E, 94, 2, Article 022415 pp. (2016) |
| [279] | Karlen, A., Man and Microbes (1996), Simon and Schuster: Simon and Schuster New York |
| [280] | Belik, V.; Geisel, T.; Brockmann, D., Natural human mobility patterns and spatial spread of infectious diseases, Phys. Rev. X, 1, 1, Article 011001 pp. (2011) |
| [281] | W. World Health Organization, SARS: How a Global Pandemic was Stopped (2006), WPRO: WPRO Geneva |
| [282] | Pastor-Satorras, R.; Castellano, C.; Van Mieghem, P.; Vespignani, A., Epidemic processes in complex networks, Rev. Modern Phys., 87, 3, 925-979 (2015) |
| [283] | Wang, Z.; Bauch, C. T.; Bhattacharyya, S.; d’Onofrio, A.; Manfredi, P.; Perc, M.; Perra, N.; Salathé, M.; Zhao, D., Statistical physics of vaccination, Phys. Rep., 664, 1-113 (2016) · Zbl 1359.92111 |
| [284] | Kiss, I.; Miller, J.; Simon, P., Mathematics of Epidemics on Networks: From Exact To Approximate Models (2017), Springer · Zbl 1373.92001 |
| [285] | Kermack, W. O.; McKendrick, A. G., A contribution to the mathematical theory of epidemics, Proc. R. Soc. London, 115, 772, 700-721 (1997) · JFM 53.0517.01 |
| [286] | Anderson, R. M.; May, R. M., Population biology of infectious diseases: Part i, Nature, 280, 5721, 361-367 (1979) |
| [287] | Funk, S.; Gilad, E.; Watkins, C.; Jansen, V. A.A., The spread of awareness and its impact on epidemic outbreaks, Proc. Natl. Acad. Sci., 106, 16, 6872-6877 (2009) · Zbl 1203.91242 |
| [288] | Funk, S.; Salathé, M.; Jansen, V. A.A., Modelling the influence of human behaviour on the spread of infectious diseases: a review, J. R. Soc. Interface, 7, 50, 1247-1256 (2010) |
| [289] | Shaw, L.; Schwartz, I., Fluctuating epidemics on adaptive networks, Phys. Rev. E, 77, Article 066101 pp. (2008) |
| [290] | Zanette, D. H.; Risau-Gusmán, S., Infection spreading in a population with evolving contacts, J. Biol. Phys., 34, 1-2, 135-148 (2008) |
| [291] | Risau-Gusman, S.; Zanette, D. H., Contact switching as a control strategy for epidemic outbreaks, J. Theoret. Biol., 257, 1, 52-60 (2009) · Zbl 1400.92534 |
| [292] | Van Segbroeck, S.; Santos, F. C.; Pacheco, J. M., Adaptive contact networks change effective disease infectiousness and dynamics, PLoS Comput. Biol., 6, 8, Article e1000895 pp. (2010) |
| [293] | Wang, B.; Cao, L.; Suzuki, H.; Aihara, K., Epidemic spread in adaptive networks with multitype agents, J. Phys. A, 44, 3, Article 035101 pp. (2010) · Zbl 1205.92068 |
| [294] | Zhong, L.; Qiu, T.; Ren, F.; Li, P.; Chen, B., Time scales of epidemic spread and risk perception on adaptive networks, Europhys. Lett., 94, 1, 18004 (2011) |
| [295] | Shaw, L.; Schwartz, I., Enhanced vaccine control of epidemics in adpative networks, Phys. Rev. E, 81, Article 046120 pp. (2010) |
| [296] | Jolad, S.; Liu, W.; Schmittmann, B.; Zia, R. K.P., Epidemic spreading on preferred degree adaptive networks, PLoS One, 7, 11, Article e48686 pp. (2012) |
| [297] | Zhou, J.; Xiao, G.; Cheong, S. A.; Fu, X.; Wong, L.; Ma, S.; Cheng, T. H., Epidemic reemergence in adaptive complex networks, Phys. Rev. E, 85, 3, Article 036107 pp. (2012) |
| [298] | Valdez, L. D.; Macri, P. A.; Braunstein, L. A., Intermittent social distancing strategy for epidemic control, Phys. Rev. E, 85, 3, Article 036108 pp. (2012) |
| [299] | Shai, S.; Dobson, S., Coupled adaptive complex networks, Phys. Rev. E, 87, 4, Article 042812 pp. (2013) |
| [300] | Youssef, M.; Scoglio, C., Mitigation of epidemics in contact networks through optimal contact adaptation, Math. Biosci. Eng., 10, 4, 1227-1251 (2013) · Zbl 1273.92062 |
| [301] | Tunc, I.; Shaw, L. B., Effects of community structure on epidemic spread in an adaptive network, Phys. Rev. E, 90, 2, Article 022801 pp. (2014) |
| [302] | Rattana, P.; Berthouze, L.; Kiss, I. Z., Impact of constrained rewiring on network structure and node dynamics, Phys. Rev. E, 90, 5, Article 052806 pp. (2014) |
| [303] | Zhang, H.-F.; Xie, J.-R.; Tang, M.; Lai, Y.-C., Suppression of epidemic spreading in complex networks by local information based behavioral responses, Chaos, 24, 4, Article 043106 pp. (2014) · Zbl 1361.92074 |
| [304] | Zhou, Y.; Xia, Y., Epidemic spreading on weighted adaptive networks, Physica A, 399, 16-23 (2014) · Zbl 1395.92181 |
| [305] | Yang, H.; Tang, M.; Gross, T., Large epidemic thresholds emerge in heterogeneous networks of heterogeneous nodes, Sci. Rep., 5, 1, 13122 (2015) |
| [306] | Szabó-Solticzky, A.; Berthouze, L.; Kiss, I. Z.; Simon, P. L., Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis, J. Math. Biol., 72, 5, 1153-1176 (2015) · Zbl 1333.05276 |
| [307] | Britton, T.; Juher, D.; Saldaña, J., A network epidemic model with preventive rewiring: Comparative analysis of the initial phase, Bull. Math. Biol., 78, 12, 2427-2454 (2016) · Zbl 1361.92063 |
| [308] | Ogura, M.; Preciado, V. M., Epidemic processes over adaptive state-dependent networks, Phys. Rev. E, 93, 6, Article 062316 pp. (2016) |
| [309] | Demirel, G.; Barter, E.; Gross, T., Dynamics of epidemic diseases on a growing adaptive network, Sci. Rep., 7, 1, 42352 (2017) |
| [310] | Ball, F.; Britton, T.; Leung, K. Y.; Sirl, D., A stochastic sir network epidemic model with preventive dropping of edges, J. Math. Biol., 78, 6, 1875-1951 (2019) · Zbl 1415.92167 |
| [311] | Gross, T.; Kevrekidis, I. G., Robust oscillations in sis epidemics on adaptive networks: Coarse-graining by automated moment closure, Europhys. Lett., 82, 3, 38004 (2008) |
| [312] | Scarpino, S. V.; Allard, A.; Hébert-Dufresne, L., The effect of a prudent adaptive behaviour on disease transmission, Nat. Phys., 12, 11, 1042-1046 (2016) |
| [313] | Boccaletti, S.; Almendral, J. A.; Guan, S.; Leyva, I.; Liu, Z.; Sendiña-Nadal, I.; Wang, Z.; Zou, Y., Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization, Phys. Rep., 660 (2016) · Zbl 1359.34048 |
| [314] | D’Souza, R. M.; Gómez-Gardeñes, J.; Nagler, J.; Arenas, A., Explosive phenomena in complex networks, Adv. Phys., 68, 3, 123-223 (2019) |
| [315] | Marceau, V.; Noël, P.-A.; Hébert-Dufresne, L.; Allard, A.; Dubé, L. J., Adaptive networks: Coevolution of disease and topology, Phys. Rev. E, 82, 3, Article 036116 pp. (2010) |
| [316] | Gräser, O.; Hui, P.; Xu, C., Separatrices between healthy and endemic states in an adaptive epidemic model, Physica A, 390, 5, 906-913 (2011) |
| [317] | Kuehn, C., A mathematical framework for critical transitions: Normal forms, variance and applications, J. Nonlinear Sci., 23, 3, 457-510 (2012) · Zbl 1282.34062 |
| [318] | Yang, H.; Tang, M.; Zhang, H.-F., Efficient community-based control strategies in adaptive networks, New J. Phys., 14, 12, Article 123017 pp. (2012) |
| [319] | Juher, D.; Ripoll, J.; Saldaña, J., Outbreak analysis of an sis epidemic model with rewiring, J. Math. Biol., 67, 2, 411-432 (2012) · Zbl 1402.92393 |
| [320] | Rogers, T.; Clifford-Brown, W.; Mills, C.; Galla, T., Stochastic oscillations of adaptive networks: application to epidemic modelling, J. Stat. Mech. Theory Exp., 2012, 08, P08018 (2012) |
| [321] | Wieland, S.; Aquino, T.; Nunes, A., The structure of coevolving infection networks, Europhys. Lett., 97, 1, 18003 (2012) |
| [322] | Zhou, J.; Xiao, G.; Chen, G., Link-based formalism for time evolution of adaptive networks, Phys. Rev. E, 88, 3, Article 032808 pp. (2013) |
| [323] | Guo, D.; Trajanovski, S.; van de Bovenkamp, R.; Wang, H.; Van Mieghem, P., Epidemic threshold and topological structure of susceptible-infectious-susceptible epidemics in adaptive networks, Phys. Rev. E, 88, 4, Article 042802 pp. (2013) |
| [324] | Trajanovski, S.; Guo, D.; Van Mieghem, P., From epidemics to information propagation: Striking differences in structurally similar adaptive network models, Phys. Rev. E, 92, 3, Article 030801 pp. (2015) |
| [325] | Kuehn, C.; Zschaler, G.; Gross, T., Early warning signs for saddle-escape transitions in complex networks, Sci. Rep., 5, 13190 (2015) |
| [326] | Yang, H.; Rogers, T.; Gross, T., Network inoculation: Heteroclinics and phase transitions in an epidemic model, Chaos, 26, 8, Article 083116 pp. (2016) |
| [327] | Kattis, A. A.; Holiday, A.; Stoica, A.-A.; Kevrekidis, I. G., Modeling epidemics on adaptively evolving networks: A data-mining perspective, Virulence, 7, 2, 153-162 (2016) |
| [328] | Horstmeyer, L.; Kuehn, C.; Thurner, S., Network topology near criticality in adaptive epidemics, Phys. Rev. E, 98, Article 042313 pp. (2018) |
| [329] | Sahneh, F. D.; Vajdi, A.; Melander, J.; Scoglio, C. M., Contact adaption during epidemics: A multilayer network formulation approach, IEEE Trans. Netw. Sci. Eng., 6, 1, 16-30 (2019) |
| [330] | Zhang, X.; Shan, C.; Jin, Z.; Zhu, H., Complex dynamics of epidemic models on adaptive networks, J. Differential Equations, 266, 1, 803-832 (2019) · Zbl 1410.35259 |
| [331] | Kuehn, C.; Bick, C., A universal route to explosive phenomena, Sci. Adv., 7, 16, Article eabe3824 pp. (2021) |
| [332] | Mancastroppa, M.; Burioni, R.; Colizza, V.; Vezzani, A., Active and inactive quarantine in epidemic spreading on adaptive activity-driven networks, Phys. Rev. E, 102, 2, Article 020301 pp. (2020) |
| [333] | Meloni, S.; Perra, N.; Arenas, A.; Gómez, S.; Moreno, Y.; Vespignani, A., Modeling human mobility responses to the large-scale spreading of infectious diseases, Sci. Rep., 1, 1, 62 (2011) |
| [334] | Wang, Z.; Andrews, M. A.; Wu, Z.-X.; Wang, L.; Bauch, C. T., Coupled disease-behavior dynamics on complex networks: A review, Phys. Life Rev., 15, 1-29 (2015) |
| [335] | Wang, W.; Liu, Q.-H.; Cai, S.-M.; Tang, M.; Braunstein, L. A.; Stanley, H. E., Suppressing disease spreading by using information diffusion on multiplex networks, Sci. Rep., 6, 1, 29259 (2016) |
| [336] | Kiss, I. Z.; Cassell, J.; Recker, M.; Simon, P. L., The impact of information transmission on epidemic outbreaks, Math. Biosci., 225, 1, 1-10 (2010) · Zbl 1188.92033 |
| [337] | Granell, C.; Gómez, S.; Arenas, A., Dynamical interplay between awareness and epidemic spreading in multiplex networks, Phys. Rev. Lett., 111, 12, Article 128701 pp. (2013) |
| [338] | Wang, W.; Tang, M.; Yang, H.; u. Younghae Do, P. L.; Lai, Y.-C.; Lee, G., Asymmetrically interacting spreading dynamics on complex layered networks, Sci. Rep., 4, 1, 5097 (2014) |
| [339] | Andrews, M. A.; Bauch, C. T., The impacts of simultaneous disease intervention decisions on epidemic outcomes, J. Theoret. Biol., 395, 1-10 (2016) · Zbl 1343.92456 |
| [340] | Böttcher, L.; Nagler, J.; Herrmann, H., Critical behaviors in contagion dynamics, Phys. Rev. Lett., 118, 8, Article 088301 pp. (2017) |
| [341] | Pires, M. A.; Oestereich, A. L.; Crokidakis, N., Sudden transitions in coupled opinion and epidemic dynamics with vaccination, J. Stat. Mech. Theory Exp., 2018, 5, Article 053407 pp. (2018) · Zbl 1459.92141 |
| [342] | Zhan, X.-X.; Liu, C.; Zhou, G.; Zhang, Z.-K.; Sun, G.-Q.; Zhu, J. J.; Jin, Z., Coupling dynamics of epidemic spreading and information diffusion on complex networks, Appl. Math. Comput., 332, 437-448 (2018) · Zbl 1427.92097 |
| [343] | Evans, J. C.; Silk, M. J.; Boogert, N. J.; Hodgson, D. J., Infected or informed? social structure and the simultaneous transmission of information and infectious disease, Oikos, 129, 9, 1271-1288 (2020) |
| [344] | Wang, W.; Liu, Q.-H.; Liang, J.; Hu, Y.; Zhou, T., Coevolution spreading in complex networks, Phys. Rep., 820, 1-51 (2019) |
| [345] | Mohamadou, Y.; Halidou, A.; Kapen, P. T., A review of mathematical modeling, artificial intelligence and datasets used in the study, prediction and management of covid-19, Appl. Intell., 50, 11, 3913-3925 (2020) |
| [346] | Silk, M. J.; Fefferman, N. H., The role of social structure and dynamics in the maintenance of endemic disease, Behav. Ecol. Sociobiol., 75, 8, 122 (2021) |
| [347] | Martens, E. A.; Klemm, K., Cyclic structure induced by load fluctuations in adaptive transportation networks, 147-155 (2019) · Zbl 1469.90051 |
| [348] | Reichold, J.; Stampanoni, M.; Lena Keller, A.; Buck, A.; Jenny, P.; Weber, B., Vascular graph model to simulate the cerebral blood flow in realistic vascular networks, J. Cereb. Blood Flow Metab., 29, 8, 1429-1443 (2009) |
| [349] | Kuehn, C.; Mölter, J., The influence of a transport process on the epidemic threshold, J. Math. Biol., 85, 62 (2022) · Zbl 1504.92141 |
| [350] | Lenton, T. M.; Held, H.; Kriegler, E.; Hall, J. W.; Lucht, W.; Rahmstorf, S.; Schellnhuber, H. J., Tipping elements in the earth’s climate system, Proc. Natl. Acad. Sci. USA, 105, 6, 1786-1793 (2008) · Zbl 1215.86004 |
| [351] | Wunderling, N.; Donges, J. F.; Kurths, J.; Winkelmann, R., Interacting tipping elements increase risk of climate domino effects under global warming, Earth Syst. Dyn., 12, 2, 601-619 (2021) |
| [352] | Deco, G.; Jirsa, V.; McIntosh, A. R.; Sporns, O.; Kotter, R., Key role of coupling, delay, and noise in resting brain fluctuations, Proc. Natl. Acad. Sci., 106, 25, 10302-10307 (2009) |
| [353] | Wu, J., Introduction To Neural Dynamics and Signal Transmission Delay, Vol. 6 (2001), Walter de Gruyter: Walter de Gruyter Berlin, Boston · Zbl 0977.34069 |
| [354] | Soriano, M. C.; García-Ojalvo, J.; Mirasso, C. R.; Fischer, I., Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers, Rev. Modern Phys., 85, 1, 421-470 (2013) |
| [355] | Giacomelli, G.; Politi, A.; Yanchuk, S., Modeling active optical networks, Physica D, 412, Article 132631 pp. (2020) · Zbl 1487.78024 |
| [356] | Eurich, C. W.; Pawelzik, K.; Ernst, U.; Cowan, J. D.; Milton, J. G., Dynamics of self-organized delay adaptation, Phys. Rev. Lett., 82, 7, 1594-1597 (1999) |
| [357] | Lücken, L.; Rosin, D. P.; Worlitzer, V. M.; Yanchuk, S., Pattern reverberation in networks of excitable systems with connection delays, Chaos, 27, 1, 13114 (2017) · Zbl 1390.92014 |
| [358] | Paugam-Moisy, H.; Martinez, R.; Bengio, S., Delay learning and polychronization for reservoir computing, Neurocomputing, 71, 7-9, 1143-1158 (2008) |
| [359] | Kempter, R.; Gerstner, W.; van Hemmen, J. L.; Wagner, H., Temporal coding in the sub-millisecond range: Model of barn owl auditory pathway, (Touretzky, D. S.; Mozer, M.; Hasselmo, M. E., Advances in Neural Information Processing Systems, Vol. 8. Advances in Neural Information Processing Systems, Vol. 8, NIPS, Denver, CO, USA, November (1995), 27-30 (1995), MIT Press), 124-130, URL http://papers.nips.cc/paper/1157-temporal-coding-in-the-sub-millisecond-range-model-of-barn-owl-auditory-pathway |
| [360] | Park, S. H.; Lefebvre, J., Synchronization and resilience in the kuramoto white matter network model with adaptive state-dependent delays, J. Math. Neurosci., 10, 1, 1-25 (2020) · Zbl 1448.92022 |
| [361] | Fields, R. D., A new mechanism of nervous system plasticity: activity-dependent myelination, Nat. Rev. Neurosci., 16, 12, 756-767 (2015) |
| [362] | Pajevic, S.; Basser, P. J.; Fields, R. D., Role of myelin plasticity in oscillations and synchrony of neuronal activity, Neuroscience, 276, 135-147 (2014) |
| [363] | Almeida, R. G.; Lyons, D. A., On myelinated axon plasticity and neuronal circuit formation and function, J. Neurosci., 37, 42, 10023-10034 (2017) |
| [364] | Bechler, M. E.; Swire, M.; Ffrench-Constant, C., Intrinsic and adaptive myelination-a sequential mechanism for smart wiring in the brain, Dev. Neurobiol., 78, 2, 68-79 (2018) |
| [365] | Monje, M., Myelin plasticity and nervous system function, Ann. Rev. Neurosci., 41, 61-76 (2018) |
| [366] | Senn, W.; Schneider, M.; Ruf, B., Activity-dependent development of axonal and dendritic delays, or, why synaptic transmission should be unreliable, Neural Comput., 14, 3, 583-619 (2002) · Zbl 0987.92010 |
| [367] | Fields, R. D., Change in the brain’s white matter, Science, 330, 6005, 768-769 (2010) |
| [368] | Hartung, F.; Krisztin, T.; Walther, H. O.; Wu, J., Chapter 5 functional differential equations with state-dependent delays: Theory and applications, (Handbook of Differential Equations: Ordinary Differential Equations (2006)) |
| [369] | Pecora, L. M.; Carroll, T. L., Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80, 10, 2109-2112 (1998) |
| [370] | Jaros, P.; Maistrenko, Y.; Kapitaniak, T., Chimera states on the route from coherence to rotating waves, Phys. Rev. E, 91, 2, Article 022907 pp. (2015) |
| [371] | Fell, J.; Axmacher, N., The role of phase synchronization in memory processes, Nat. Rev. Neurosci., 12, 2, 105-118 (2011) |
| [372] | Hammond, C.; Bergman, H.; Brown, P., Pathological synchronization in parkinson’s disease: networks, models and treatments, Trends Neurosci., 30, 357-364 (2007) |
| [373] | Jiruska, P.; de Curtis, M.; Jefferys, J. G.R.; Schevon, C. A.; Schiff, S. J.; Schindler, K., Synchronization and desynchronization in epilepsy: controversies and hypotheses, J. Physiol., 591, 4, 787-797 (2013) |
| [374] | Tass, P. A.; Popovych, O. V., Unlearning tinnitus-related cerebral synchrony with acoustic coordinated reset stimulation: theoretical concept and modelling, Biol. Cybernet., 106, 1, 27-36 (2012) |
| [375] | Uhlhaas, P.; Pipa, G.; Lima, B.; Melloni, L.; Neuenschwander, S.; Nikolic, D.; Singer, W., Neural synchrony in cortical networks: history, concept and current status, Front. Integr. Neurosci., 3, 17 (2009) |
| [376] | Karbowski, J.; Ermentrout, G. B., Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators, Phys. Rev. E, 65, Article 031902 pp. (2002) |
| [377] | Ha, S. Y.; Noh, S. E.; Park, J., Synchronization of kuramoto oscillators with adaptive couplings, SIAM J. Appl. Dyn. Syst., 15, 1, 162-194 (2016) · Zbl 1393.34052 |
| [378] | Ha, S. Y.; Lee, J.; Li, Z.; Park, J., Emergent dynamics of kuramoto oscillators with adaptive couplings: conservation law and fast learning, SIAM J. Appl. Dyn. Syst., 17, 2, 1560-1588 (2018) · Zbl 1401.70030 |
| [379] | Ha, S.; Kim, D.; Moon, B., Interplay of random inputs and adaptive couplings in the winfree model, Commun. Pure Appl. Anal., 22, 11, 3975-4006 (2021) · Zbl 1482.92125 |
| [380] | Berner, R.; Yanchuk, S., Synchronization in networks with heterogeneous adaptation rules and applications to distance-dependent synaptic plasticity, Front. Appl. Math. Stat., 7, Article 714978 pp. (2021) |
| [381] | Schöll, E., Partial synchronization patterns in brain networks, Europhys. Lett., 136, 1, 18001 (2021) |
| [382] | Baker, S. N.; Olivier, E.; Lemon, R. N., Coherent oscillations in monkey motor cortex and hand muscle EMG show task-dependent modulation, J. Physiol., 501, 1, 225-241 (1997) |
| [383] | Aoki, T., Self-organization of a recurrent network under ongoing synaptic plasticity, Neural Netw., 62, 11-19 (2015) · Zbl 1368.92013 |
| [384] | Vock, S.; Berner, R.; Yanchuk, S.; Schöll, E., Effect of diluted connectivities on cluster synchronization of adaptively coupled oscillator networks, Sci. Iran. D, 28, 3, 1669-1684 (2021) |
| [385] | Ivanchenko, M. V.; Osipov, G. V.; Shalfeev, V. D.; Kurths, J., Phase synchronization in ensembles of bursting oscillators, Phys. Rev. Lett., 93, 13, Article 134101 pp. (2004) |
| [386] | Montbrió, E.; Kurths, J.; Blasius, B., Synchronization of two interacting populations of oscillators, Phys. Rev. E, 70, 5, 4 (2004) |
| [387] | Yue, W.; Smith, L. D.; Gottwald, G. A., Model reduction for the kuramoto-sakaguchi model: The importance of nonentrained rogue oscillators, Phys. Rev. E, 101, 6, 1-14 (2020) |
| [388] | Patzauer, M.; Krischer, K., Self-organized multifrequency clusters in an oscillating electrochemical system with strong nonlinear coupling, Phys. Rev. Lett., 126, 19, Article 194101 pp. (2021) |
| [389] | Berner, R., Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators (2021), Springer: Springer Cham, (Springer Theses) · Zbl 1469.34001 |
| [390] | Feketa, P.; Schaum, A.; Meurer, T., Stability of cluster formations in adaptive kuramoto networks, IFAC-PapersOnLine, 54, 9, 14-19 (2021) |
| [391] | Ito, J.; Kaneko, K., Spontaneous structure formation in a network of chaotic units with variable connection strengths, Phys. Rev. Lett., 88, 2, Article 028701 pp. (2001) |
| [392] | Ito, J.; Kaneko, K., Spontaneous structure formation in a network of dynamic elements, Phys. Rev. E, 67, 4, Article 046226 pp. (2003) |
| [393] | Stam, C. J.; Hillebrand, A.; Wang, H.; Van Mieghem, P., Emergence of modular structure in a large-scale brain network with interactions between dynamics and connectivity, Front. Comput. Neurosci., 4, 133 (2010) |
| [394] | Assenza, S.; Gutiérrez, R.; Gómez-Gardeñes, J.; Latora, V.; Boccaletti, S., Emergence of structural patterns out of synchronization in networks with competitive interactions, Sci. Rep., 1, 99 (2011) |
| [395] | Yuan, W. J.; Zhou, C., Interplay between structure and dynamics in adaptive complex networks: Emergence and amplification of modularity by adaptive dynamics, Phys. Rev. E, 84, 1, Article 016116 pp. (2011) |
| [396] | Aoki, T.; Aoyagi, T., Scale-free structures emerging from co-evolution of a network and the distribution of a diffusive resource on it, Phys. Rev. Lett., 109, 20, Article 208702 pp. (2012) |
| [397] | Winkler, M.; Butscher, S.; Kinzel, W., Pulsed chaos synchronization in networks with adaptive couplings, Phys. Rev. E, 86, 1, Article 016203 pp. (2012) |
| [398] | Aoki, T.; Yawata, K.; Aoyagi, T., Self-organization of complex networks as a dynamical system, Phys. Rev. E, 91, 1, Article 012908 pp. (2015) |
| [399] | Botella-Soler, V.; Glendinning, P., Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems, Europhys. Lett., 97, 5, 50004 (2012) |
| [400] | Botella-Soler, V.; Glendinning, P., Hierarchy and polysynchrony in an adaptive network, Phys. Rev. E, 89, 6, Article 062809 pp. (2014) |
| [401] | Makarov, V.; Koronovskii, A.; Maksimenko, V.; Hramov, A.; Moskalenko, O.; Boccaletti, S., Emergence of a multilayer structure in adaptive networks of phase oscillators, Chaos Solitons Fractals, 84, 23-30 (2016) · Zbl 1355.34065 |
| [402] | Avalos-Gaytán, V.; Almendral, J. A.; Papo, D.; Schaeffer, S. E.; Boccaletti, S., Assortative and modular networks are shaped by adaptive synchronization processes, Phys. Rev. E, 86, 1, Article 015101 pp. (2012) |
| [403] | Meunier, D.; Lambiotte, R.; Bullmore, E. T., Modular and hierarchically modular organization of brain networks, Front. Neurosci., 4, 200 (2010) |
| [404] | Ashourvan, A.; Telesford, Q. K.; Verstynen, T.; Vettel, J. M.; Bassett, D. S., Multi-scale detection of hierarchical community architecture in structural and functional brain networks, PLoS One, 14, 5, Article e0215520 pp. (2019) |
| [405] | Maistrenko, Y.; Penkovsky, B.; Rosenblum, M., Solitary state at the edge of synchrony in ensembles with attractive and repulsive interactions, Phys. Rev. E, 89, 6, Article 060901 pp. (2014) |
| [406] | Kapitaniak, T.; Kuzma, P.; Wojewoda, J.; Czolczynski, K.; Maistrenko, Y., Imperfect chimera states for coupled pendula, Sci. Rep., 4, 1, 6379 (2015) |
| [407] | Belykh, I. V.; Hasler, M., Mesoscale and clusters of synchrony in networks of bursting neurons, Chaos, 21, 1, Article 016106 pp. (2011) · Zbl 1345.92035 |
| [408] | Belykh, I. V.; Shilnikov, A., When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons, Phys. Rev. Lett., 101, Article 078102 pp. (2008) |
| [409] | Blank, D. A.; Stoop, R., Collective bursting in populations of intrinsically nonbursting neurons, Z. Naturf. a, 54, 617 (1999) |
| [410] | Stoop, R.; Blank, D.; Kern, A.; Van der Vyver, J.; Christen, M.; Lecchini, S.; Wagner, C., Collective bursting in layer IV synchronization by small thalamic inputs and recurrent connections, Brain Res. Cogn. Brain Res., 13, 293 (2002) |
| [411] | Panchuk, A.; Rosin, D. P.; Hövel, P.; Schöll, E., Synchronization of coupled neural oscillators with heterogeneous delays, Int. J. Bifurc. Chaos, 23, 12, Article 1330039 pp. (2013) · Zbl 1284.34112 |
| [412] | Schöll, E.; Hiller, G.; Hövel, P.; Dahlem, M. A., Time-delayed feedback in neurosystems, Phil. Trans. R. Soc. A, 367, 1891, 1079-1096 (2009) · Zbl 1185.34108 |
| [413] | Gast, R.; Schmidt, H.; Knösche, T. R., A mean-field description of bursting dynamics in spiking neural networks with short-term adaptation, Neural Comput., 32, 1615 (2020) · Zbl 1453.92013 |
| [414] | Izhikevich, E. M., Neural excitability, spiking and bursting, Int. J. Bifurc. Chaos, 10, 6, 1171-1266 (2000) · Zbl 1090.92505 |
| [415] | Hesse, J.; Gross, T., Self-organized criticality as a fundamental property of neural systems, Front. Syst. Neurosci., 8, 166 (2014) |
| [416] | Shew, W. L.; Clawson, W. P.; Pobst, J.; Karimipanah, Y.; Wright, N. C.; Wessel, R., Adaptation to sensory input tunes visual cortex to criticality, Nat. Phys., 11, 8, 659-663 (2015) |
| [417] | Zeraati, R.; Priesemann, V.; Levina, A., Self-organization toward criticality by synaptic plasticity, Front. Phys., 9, Article 619661 pp. (2021) |
| [418] | Kim, S. Y.; Lim, W., Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network, Cogn. Neurodyn., 12, 3, 315-342 (2018) |
| [419] | Izhikevich, E. M., Which model to use for cortical spiking neurons?, IEEE Trans. Neural Netw., 15, 5, 1063-1070 (2004) |
| [420] | Pisarchik, A. N.; Feudel, U., Control of multistability, Phys. Rep., 540, 167-218 (2014) · Zbl 1357.34105 |
| [421] | Feudel, U.; Pisarchik, A. N.; Showalter, K., Multistability and tipping: From mathematics and physics to climate and brain – minireview and preface to the focus issue, Chaos, 28, 3, Article 033501 pp. (2018) |
| [422] | Kelso, J. A.S., Multistability and metastability: understanding dynamic coordination in the brain, Philos. Trans. R. Soc. B, 367, 1591, 906-918 (2012) |
| [423] | Tass, P. A., A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations, Biol. Cybernet., 89, 2, 81-88 (2003) · Zbl 1084.92009 |
| [424] | Tass, P. A.; Adamchic, I.; Freund, H. J.; von Stackelberg, T.; Hauptmann, C., Counteracting tinnitus by acoustic coordinated reset neuromodulation, Restor. Neurol. Neurosci., 30, 2, 137-159 (2012) |
| [425] | Pfeifer, K. J.; Kromer, J. A.; Cook, A. J.; Hornbeck, T.; Lim, E. A.; Mortimer, B. J.P.; Fogarty, A. S.; Han, S. S.; Dhall, R.; Halpern, C. H.; Tass, P. A., Coordinated reset vibrotactile stimulation induces sustained cumulative benefits in parkinson’s disease, Front. Physiol., 12, Article 624317 pp. (2021) |
| [426] | Kromer, J. A.; Tass, P. A., Long-lasting desynchronization by decoupling stimulation, Phys. Rev. Res., 2, 3, Article 033101 pp. (2020) |
| [427] | Kromer, J. A.; Khaledi-Nasab, A.; Tass, P. A., Impact of number of stimulation sites on long-lasting desynchronization effects of coordinated reset stimulation, Chaos, 30, 8, Article 083134 pp. (2020) · Zbl 1445.92056 |
| [428] | Khaledi-Nasab, A.; Kromer, J. A.; Tass, P. A., Long-lasting desynchronization of plastic neural networks by random reset stimulation, Front. Physiol., 11, Article 622620 pp. (2021) |
| [429] | Seliger, P.; Young, S. C.; Tsimring, L. S., Plasticity and learning in a network of coupled phase oscillators, Phys. Rev. E, 65, 4, Article 041906 pp. (2002) · Zbl 1244.34078 |
| [430] | Chandrasekar, V. K.; Sheeba, J. H.; Subash, B.; Lakshmanan, M.; Kurths, J., Adaptive coupling induced multi-stable states in complex networks, Physica D, 267, 36-48 (2014) · Zbl 1285.34050 |
| [431] | Kasatkin, D. V.; Nekorkin, V. I., Transient circulant clusters in two-population network of kuramoto oscillators with different rules of coupling adaptation, Chaos, 31, Article 073112 pp. (2021) · Zbl 1468.34067 |
| [432] | Thamizharasan, S.; Chandrasekar, V. K.; Senthilvelan, M.; Berner, R.; Schöll, E.; Senthilkumar, D. V., Exotic states induced by coevolving connection weights and phases in complex networks, Phys. Rev. E, 105, Article 034312 pp. (2022) |
| [433] | Ratas, I.; Pyragas, K.; Tass, P. A., Multistability in a star network of kuramoto-type oscillators with synaptic plasticity, Sci. Rep., 11, 9840 (2021) |
| [434] | Kasatkin, D. V.; Nekorkin, V. I., The effect of topology on organization of synchronous behavior in dynamical networks with adaptive couplings, Eur. Phys. J. Spec. Top., 227, 1051 (2018) |
| [435] | Berner, R.; Sawicki, J.; Schöll, E., Birth and stabilization of phase clusters by multiplexing of adaptive networks, Phys. Rev. Lett., 124, 8, Article 088301 pp. (2020) |
| [436] | Berner, R.; Mehrmann, V.; Schöll, E.; Yanchuk, S., The multiplex decomposition: An analytic framework for multilayer dynamical networks, SIAM J. Appl. Dyn. Syst., 20, 4, 1752-1772 (2021) · Zbl 1485.34105 |
| [437] | Gómez-Gardeñes, J.; Gómez, S.; Arenas, A.; Moreno, Y., Explosive synchronization transitions in scale-free networks, Phys. Rev. Lett., 106, Article 128701 pp. (2011) |
| [438] | Zou, Y.; Pereira, T.; Small, M.; Liu, Z.; Kurths, J., Basin of attraction determines hysteresis in explosive synchronization, Phys. Rev. Lett., 112, Article 114102 pp. (2014) |
| [439] | Vlasov, V.; Zou, Y.; Pereira, T., Explosive synchronization is discontinuous, Phys. Rev. E, 92, Article 012904 pp. (2015) |
| [440] | Căugăru, D.; Totz, J. F.; Martens, E. A.; Engel, H., First-order synchronization transition in a large population of strongly coupled relaxation oscillators, Sci. Adv., 6, 39, Article eabb2637 pp. (2020) |
| [441] | Eom, Y.-H.; Boccaletti, S.; Caldarelli, G., Concurrent enhancement of percolation and synchronization in adaptive networks, Sci. Rep., 6, 1, 27111 (2016) |
| [442] | Kachhvah, A. D.; Dai, X.; Boccaletti, S.; Jalan, S., Interlayer hebbian plasticity induces first-order transition in multiplex networks, New J. Phys., 22, Article 122001 pp. (2020) |
| [443] | Kumar, A.; Jalan, S.; Kachhvah, A. D., Interlayer adaptation-induced explosive synchronization in multiplex networks, Phys. Rev. Res., 2, Article 023259 pp. (2020) |
| [444] | Fialkowski, J.; Yanchuk, S.; Sokolov, I. M.; Schöll, E.; Gottwald, G. A.; Berner, R., Heterogeneous nucleation in finite size adaptive dynamical networks, Phys. Rev. Lett., 130, Article 067402 pp. (2022) |
| [445] | Pruppacher, H. R.; Klett, J. D., Microphysics of Clouds and Precipitation, Atmospheric and Oceanographic Sciences Library (2010), Springer: Springer Dordrecht |
| [446] | Mullin, J. W., Crystallization (2001), Elsevier |
| [447] | Schimansky-Geier, L.; Zülicke, C.; Schöll, E., Domain formation due to ostwald ripening in bistable systems far from equilibrium, Z. Phys. B, 84, 433 (1991) |
| [448] | Gottwald, G. A., Model reduction for networks of coupled oscillators, Chaos, 25, 5, Article 053111 pp. (2015) · Zbl 1374.34106 |
| [449] | Hancock, E. J.; Gottwald, G. A., Model reduction for kuramoto models with complex topologies, Phys. Rev. E, 98, 1, Article 012307 pp. (2018) |
| [450] | Smith, L. D.; Gottwald, G. A., Chaos in networks of coupled oscillators with multimodal natural frequency distributions, Chaos, 29, Article 093127 pp. (2020) · Zbl 1423.34059 |
| [451] | Smith, L. D.; Gottwald, G. A., Model reduction for the collective dynamics of globally coupled oscillators: From finite networks to the thermodynamic limit, Chaos, 30, 9, Article 093107 pp. (2020) · Zbl 1451.34042 |
| [452] | Smith, L. D.; Gottwald, G. A., Mesoscopic model reduction for the collective dynamics of sparse coupled oscillator networks, Chaos, 31, 7, Article 073116 pp. (2021) · Zbl 1468.34048 |
| [453] | Duchet, B.; Bick, C.; Byrne, A., Mean-field approximations with adaptive coupling for networks with spike-timing-dependent plasticity (2022), bioRxiv |
| [454] | Ott, E.; Antonsen, T. M., Low dimensional behavior of large systems of globally coupled oscillators, Chaos, 18, 3, Article 037113 pp. (2008) · Zbl 1309.34058 |
| [455] | Abrams, D. M.; Strogatz, S. H., Chimera states for coupled oscillators, Phys. Rev. Lett., 93, 17, Article 174102 pp. (2004) |
| [456] | Zakharova, A., Chimera Patterns in Networks: Interplay Between Dynamics, Structure, Noise, and Delay, Understanding Complex Systems (2020), Springer: Springer Cham · Zbl 1451.93004 |
| [457] | Haugland, S. W., The changing notion of chimera states, a critical review, J. Phys. Complex., 2, 3, Article 032001 pp. (2021) |
| [458] | Motter, A. E., Nonlinear dynamics: Spontaneous synchrony breaking, Nat. Phys., 6, 3, 164-165 (2010) |
| [459] | Schöll, E., Chimera states and excitation waves in networks with complex topologies, AIP Conf. Proc., 1738, Article 210012 pp. (2016) |
| [460] | Majhi, S.; Bera, B. K.; Ghosh, D.; Perc, M., Chimera states in neuronal networks: {A} review, Phys. Life Rev., 26, 100-121 (2019) |
| [461] | Omel’chenko, O. E.; Knobloch, E., Chimerapedia: coherence-incoherence patterns in one, two and three dimensions, New J. Phys., 21, 9, Article 093034 pp. (2019) |
| [462] | Parastesh, F.; Jafari, S.; Azarnoush, H.; Shahriari, Z.; Wang, Z.; Boccaletti, S.; Perc, M., Chimeras, Phys. Rep., 898, 1-114 (2021) · Zbl 1490.34044 |
| [463] | Omel’chenko, O. E., The mathematics behind chimera states, Nonlinearity, 31, 5, R121 (2018) · Zbl 1395.34045 |
| [464] | Zhang, Y.; Motter, A. E., Mechanism for strong chimeras, Phys. Rev. Lett., 126, Article 094101 pp. (2021) |
| [465] | Hou, Y. S.; Xia, G. Q.; Jayaprasath, E.; Yue, D. Z.; Yang, W. Y.; Wu, Z. M., Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers, Opt. Commun., 433, 215-220 (2019) |
| [466] | Wang, Z.; Baruni, S.; Parastesh, F.; Jafari, S.; Ghosh, D.; Perc, M.; Hussain, I., Chimeras in an adaptive neuronal network with burst-timing-dependent plasticity, Neurocomputing, 406, 117-126 (2020) |
| [467] | Venegas-Pineda, L. G.; Jardón-Kojakhmetov, H.; Cao, M., Stable chimera states: A geometric singular perturbation approach (2023), arXiv preprint arXiv:2301.07071 |
| [468] | Kasatkin, D. V.; Klinshov, V. V.; Nekorkin, V. I., Itinerant chimeras in an adaptive network of pulse-coupled oscillators, Phys. Rev. E, 99, Article 022203 pp. (2019) |
| [469] | Ashwin, P.; Burylko, O., Weak chimeras in minimal networks of coupled phase oscillators, Chaos, 25, Article 013106 pp. (2015) · Zbl 1345.34052 |
| [470] | Boltzmann, L., Weitere studien über das wärmegleichgewicht unter gasmolekülen, sitzungberichte der kaiserlichen akademie der wissenschaften, Mathematisch-Naturwissenschaftliche Classe, 66, 262-349 (1872) |
| [471] | Fokker, A., Die mittlere energie rotierender elektrischer dipole im strahlungsfeld, Ann. Physics, 348, 4, 810-820 (1914) |
| [472] | Jeans, J., On the theory of star-streaming and the structure of the universe, Mon. Notices Royal Astron. Soc., 76, 70-84 (1915) |
| [473] | Planck, M., Über einen satz der statistischen dynamik und seine erweiterung in der quantentheorie, Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, 24, 324-341 (1917) |
| [474] | Vlasov, A., On high-frequency properties of electron gas, J. Exp. Theor. Phys., 8, 3, 291-318 (2006) |
| [475] | Cercignani, C., Mathematical Methods in Kinetic Theory (1969), Springer · Zbl 0191.25103 |
| [476] | Desai, R.; Zwanzig, R., Statistical mechanics of a nonlinear stochastic model, J. Stat. Phys., 19, 1-24 (1978) |
| [477] | Winfree, A., Biological rhythms and the behavior of populations of coupled oscillators, J. Theoret. Biol., 16, 1, 15-42 (1967) |
| [478] | Somers, D.; Kopell, N., Rapid synchronization through fast threshold modulation, Biol. Cybernet., 68, 5, 393-407 (1993) |
| [479] | Hopfield, J., Neural networks and physical systems with emergent collective computational properties, Proc. Nat. Acad. Sci. USA, 79, 2554-2558 (1982) · Zbl 1369.92007 |
| [480] | Cucker, F.; Smale, S., Emergent behavior in flocks, IEEE Trans. Automat. Control, 52, 5, 852-862 (2007) · Zbl 1366.91116 |
| [481] | Golse, F., On the dynamics of large particle systems in the mean field limit, (Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity (2016), Springer), 1-144 |
| [482] | Dobrushin, R., Vlasov equations, Funct. Anal. Appl., 13, 115-123 (1979) · Zbl 0422.35068 |
| [483] | Neunzert, H., An introduction to the nonlinear Boltzmann-Vlasov equation, (Kinetic Theories and the Boltzmann Equation (1984), Springer), 60-110 · Zbl 0575.76120 |
| [484] | Arenas, A.; Diaz-Guilera, A.; Kurths, J.; Moreno, Y.; Zhou, C., Synchronization in complex networks, Phys. Rep., 469, 3, 93-153 (2008) |
| [485] | Lovász, L., Large Networks and Graph Limits (2012), AMS · Zbl 1292.05001 |
| [486] | Chiba, H.; Medvedev, G., The mean field analysis for the Kuramoto model on graphs I. the mean field equation and transition point formulas, Discr. Cont. Dyn. Syst. A, 39, 1, 131-155 (2019) · Zbl 1406.34064 |
| [487] | Kaliuzhnyi-Verbovetskyi, D.; Medvedev, G., The mean field equation for the Kuramoto model on graph sequences with non-Lipschitz limit, SIAM J. Math. Anal., 50, 3, 2441-2465 (2018) · Zbl 1406.35096 |
| [488] | Bick, C.; Sclosa, D., Mean-field limits of phase oscillator networks and their symmetries, 1-28 (2021), arXiv:2110.13686 |
| [489] | Chiba, H.; Medvedev, G., The mean field analysis for the Kuramoto model on graphs II. asymptotic stability of the incoherent state, center manifold reduction, and bifurcations, Discr. Cont. Dyn. Syst. A, 39, 7, 3897 (2019) · Zbl 1420.34062 |
| [490] | Chiba, H.; Medvedev, G.; Mizuhara, M., Bifurcations in the Kuramoto model on graphs, Chaos, 28, 7, Article 073109 pp. (2018) · Zbl 1407.34053 |
| [491] | Backhausz, A.; Szegedy, B., Action convergence of operators and graphs, Canad. J. Math., 74, 1, 72-121 (2022) · Zbl 1482.05187 |
| [492] | Kuehn, C., Network dynamics on graphops, New J. Phys., 22, 5, Article 053030 pp. (2020) |
| [493] | Gkogkas, M.; Kuehn, C., Graphop mean-field limits for Kuramoto-type models, SIAM J. Appl. Dyn. Syst., 21, 1, 248-283 (2022) · Zbl 1483.35270 |
| [494] | Kuehn, C.; Xu, C., Vlasov equations on digraph measures, J. Differ. Eq., 339, 261-349 (2022) · Zbl 1498.05251 |
| [495] | Ayi, N.; Duteil, N., Mean-field and graph limits for collective dynamics models with time-varying weights, J. Differ. Eq., 299, 65-110 (2021) · Zbl 1472.34084 |
| [496] | Duteil, N., Mean-field limit of collective dynamics with time-varying weights, Netw. Heterog. Media, 17, 2, 129-161 (2022) · Zbl 1497.37011 |
| [497] | Risken, H., The Fokker-Planck Equation (1996), Springer · Zbl 0866.60071 |
| [498] | Frank, T., Nonlinear Fokker-Planck Equations: Fundamentals and Applications (2005), Springer · Zbl 1071.82001 |
| [499] | Pavliotis, G., Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations (2014), Springer · Zbl 1318.60003 |
| [500] | Chaintron, L.; Diez, A., Propagation of chaos: a review of models, methods and applications, 1-238 (2021), arXiv:2106.14812 |
| [501] | Socha, L., Linearization Methods for Stochastic Dynamic Systems (2008), Springer · Zbl 1145.60034 |
| [502] | Kuehn, C., Moment closure - a brief review, (Schöll, E.; Klapp, S.; Hövel, P., Control of Self-Organizing Nonlinear Systems (2016), Springer), 253-271 |
| [503] | Horstmeyer, L.; Kuehn, C.; Thurner, S., Balancing quarantine and self-distancing measures in adaptive epidemic networks, Bull. Math. Biol., 84, 8, 79 (2022) · Zbl 1497.92153 |
| [504] | Brauer, F.; Castillo-Chávez, C., Mathematical Models in Population Biology and Epidemiology (2001), Springer · Zbl 0967.92015 |
| [505] | Brauer, F.; van den Driessche, P.; Wu, J., Mathematical Epidemiology (2008), Springer · Zbl 1159.92034 |
| [506] | Keeling, M.; Eames, K., Networks and epidemic models, J. R. Soc. Interface, 2, 4, 295-307 (2005) |
| [507] | Rand, D., Correlation equations and pair approximations for spatial ecologies, CWI Q., 12, 3, 329-368 (1999) · Zbl 1001.92552 |
| [508] | Taylor, M.; Simon, P.; Green, D.; House, T.; Kiss, I., From Markovian to pairwise epidemic models and the performance of moment closure approximations, J. Math. Biol., 64, 1021-1042 (2012) · Zbl 1252.92051 |
| [509] | Levermore, C., Moment closure hierarchies for kinetic theories, J. Stat. Phys., 83, 5, 1021-1065 (1996) · Zbl 1081.82619 |
| [510] | Raghib, M.; Hill, N.; Dieckmann, U., A multiscale maximum entropy moment closure for locally regulated space-time point process models of population dynamics, J. Math. Biol., 62, 605-653 (2011) · Zbl 1232.92074 |
| [511] | Rogers, T., Maximum entropy moment-closure for stochastic systems on networks, J. Stat. Mech., 2011, P05007 (2011) |
| [512] | Gleeson, J., High-accuracy approximation and binary-state dynamics on networks, Phys. Rev. Lett., 107, Article 068701 pp. (2011) |
| [513] | Gleeson, J., Binary-state dynamics on complex networks: pair approximation and beyond, Phys. Rev. X, 3, 2, Article 021004 pp. (2013) |
| [514] | Moretti, P.; Liu, S.; Baronchelli, A.; Pastor-Satorras, R., Heterogenous mean-field analysis of a generalized voter-like model on networks, Eur. Phys. J. B, 85, 3, 1-6 (2012) |
| [515] | Porter, M.; Gleeson, J., Dynamical Systems on Networks: A Tutorial, Frontiers in Applied Dynamical Systems: Reviews and Tutorials (2016), Springer · Zbl 1369.34001 |
| [516] | Pugliese, E.; Castellano, C., Heterogeneous pair approximation for voter models on networks, Europhys. Lett., 88, Article 58004 pp. (2009) |
| [517] | Vazquez, F.; Eguíluz, V., Analytical solution of the voter model on uncorrelated networks, New J. Phys., 10, Article 063011 pp. (2008) |
| [518] | Liggett, T., Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (2013), Springer |
| [519] | Noël, P.-A.; Davoudi, B.; Brunham, R.; amd B. Pourbohloul, L. D., Time evolution of epidemic disease on finite and infinite networks, Phys. Rev. E, 79, Article 026101 pp. (2009) |
| [520] | Kaliuzhnyi-Verbovetskyi, D.; Medvedev, G., The semilinear heat equation on sparse random graphs, SIAM J. Math. Anal., 49, 2, 1333-1355 (2017) · Zbl 1377.34048 |
| [521] | Medvedev, G., The nonlinear heat equation on W-random graphs, Arch. Ration. Mech. Anal., 212, 3, 781-803 (2014) · Zbl 1293.35333 |
| [522] | Medvedev, G., Small-world networks of Kuramoto oscillators, Physica D, 266, 13-22 (2014) · Zbl 1286.34076 |
| [523] | Gkogkas, M.; Kuehn, C.; Xu, C., Continuum limits for adaptive network dynamics, Commmun. Math. Sci., 21, 1, 83-106 (2023) · Zbl 1539.35269 |
| [524] | Kuehn, C., Multiple Time Scale Dynamics (2015), Springer · Zbl 1335.34001 |
| [525] | Fenichel, N., Geometric singular perturbation theory for ordinary differential equations, J. Differ. Eq., 31, 53-98 (1979) · Zbl 0476.34034 |
| [526] | Jones, C., Geometric singular perturbation theory, (Dynamical Systems (Montecatini Terme, 1994). Dynamical Systems (Montecatini Terme, 1994), Lect. Notes Math., vol. 1609 (1995), Springer), 44-118 · Zbl 0840.58040 |
| [527] | Kaper, T., An introduction to geometric methods and dynamical systems theory for singular perturbation problems. analyzing multiscale phenomena using singular perturbation methods, (Cronin, J.; O’Malley, R., Analyzing Multiscale Phenomena using Singular Perturbation Methods (1999), Springer), 85-131 |
| [528] | Wechselberger, M., Geometric Singular Perturbation Theory beyond the Standard Form (2020), Springer · Zbl 1484.34001 |
| [529] | Fenichel, N., Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J., 21, 193-225 (1971) · Zbl 0246.58015 |
| [530] | Tikhonov, A., Systems of differential equations containing small small parameters in the derivatives, Mat. Sbornik N. S., 31, 575-586 (1952) · Zbl 0048.07101 |
| [531] | Ha, S.; Lee, J.; Li, Z.; Park, J., Emergent dynamics of Kuramoto oscillators with adaptive couplings: conservation law and fast learning, SIAM J. Appl. Dyn. Syst., 17, 2, 1560-1588 (2018) · Zbl 1401.70030 |
| [532] | Jardon-Kojakhmetov, H.; Kuehn, C., Geometric desingularization of consensus dynamics with a dynamic weight, J. Nonlinear Sci., 30, 6, 2737-2786 (2020) · Zbl 1514.34094 |
| [533] | Dumortier, F.; Roussarie, R., (Canard Cycles and Center Manifolds. Canard Cycles and Center Manifolds, Memoirs Amer. Math. Soc., vol. 121 (1996), AMS) · Zbl 0851.34057 |
| [534] | Krupa, M.; Szmolyan, P., Extending slow manifolds near transcritical and pitchfork singularities, Nonlinearity, 14, 1473-1491 (2001) · Zbl 0998.34039 |
| [535] | Bender, C.; Orszag, S., Asymptotic Methods and Perturbation Theory (1999), Springer |
| [536] | Kevorkian, J.; Cole, J., Multiple Scale and Singular Perturbation Methods (1996), Springer · Zbl 0846.34001 |
| [537] | Jager, E. D.; Furu, J., The Theory of Singular Perturbations (1996), North-Holland |
| [538] | Mishchenko, E.; Rozov, N., Differential Equations with Small Parameters and Relaxation Oscillations (Translated from Russian) (1980), Plenum Press · Zbl 0482.34004 |
| [539] | Jardon-Kojakhmetov, H.; Kuehn, C., A survey on the blow-up method for fast-slow systems, contemporary mathematics, (IV Meeting ReuniÓN de MatemáTicos Mexicanos En El Mundo (2021), AMS), 115-116 · Zbl 1506.34003 |
| [540] | Krupa, M.; Szmolyan, P., Extending geometric singular perturbation theory to nonhyperbolic points - fold and canard points in two dimensions, SIAM J. Math. Anal., 33, 2, 286-314 (2001) · Zbl 1002.34046 |
| [541] | Jones, C.; Kopell, N., Tracking invariant manifolds with differential forms in singularly perturbed systems, J. Differ. Equ., 108, 1, 64-88 (1994) · Zbl 0796.34038 |
| [542] | Desroches, M.; Krauskopf, B.; Osinga, H., Numerical continuation of canard orbits in slow-fast dynamical systems, Nonlinearity, 23, 3, 739-765 (2010) · Zbl 1191.34072 |
| [543] | Gear, C.; Kaper, T.; Kevrikidis, I.; Zagaris, A., Projecting to a slow manifold: singularly perturbed systems and legacy codes, SIAM J. Appl. Dyn. Syst., 4, 3, 711-732 (2005) · Zbl 1170.34343 |
| [544] | Guckenheimer, J.; Kuehn, C., Computing slow manifolds of saddle-type, SIAM J. Appl. Dyn. Syst., 8, 3, 854-879 (2009) · Zbl 1176.37026 |
| [545] | Kaper, H.; Kaper, T., Asymptotic analysis of two reduction methods for systems of chemical reactions, Physica D, 165, 66-93 (2002) · Zbl 1036.80007 |
| [546] | Benoît, E.; Callot, J.; Diener, F.; Diener, M., Chasse au canards, Collect. Math., 31, 37-119 (1981) · Zbl 0529.34046 |
| [547] | Eckhaus, W., (Relaxation oscillations including a standard chase on French ducks. Relaxation oscillations including a standard chase on French ducks, Lecture Notes in Mathematics, vol. 985 (1983)), 449-494 · Zbl 0509.34037 |
| [548] | Engel, M.; Kuehn, C., Blow-up analysis of fast-slow PDEs with loss of hyperbolicity, 1-35 (2020), arXiv:2007.09973 |
| [549] | Hummel, F.; Kuehn, C., Slow manifolds for infinite-dimensional evolution equations, Comment. Math. Helv., 97, 1, 61-132 (2022) · Zbl 1487.35035 |
| [550] | Engel, F. H.M.; Kuehn, C., Connecting a direct and a Galerkin approach to slow manifolds in infinite dimensions, Proc. Amer. Math. Soc., 8, 252-266 (2021) · Zbl 1481.37092 |
| [551] | Jain, S.; Krishna, S., Autocatalytic sets and the growth of complexity in an evolutionary model, Phys. Rev. Lett., 81, 25, 5684-5687 (1998) |
| [552] | Jain, S.; Krishna, S., Graph theory and the evolution of autocatalytic networks, (Bornholdt, S.; Schuster, H., Handbook of Graphs and Networks: From the Genome To the Internet (2006), Wiley), 355-395 |
| [553] | Kauffman, S., Autocatalytic sets of proteins, J. Theoret. Biol., 119, 1, 1-24 (1986) |
| [554] | Kuehn, C., Time-scale and noise optimality in self-organized critical adaptive networks, Phys. Rev. E, 85, 2, Article 026103 pp. (2012) |
| [555] | Guckenheimer, J.; Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (1983), Springer: Springer New York, NY · Zbl 0515.34001 |
| [556] | Kuznetsov, Y., Elements of Applied Bifurcation Theory (2004), Springer: Springer New York, NY · Zbl 1082.37002 |
| [557] | Strogatz, S., Nonlinear Dynamics and Chaos (2000), Westview Press |
| [558] | Jüttner, B.; Martens, E. A., Complex dynamics in adaptive phase oscillator networks (2022), arXiv preprint arXiv:2209.10514 |
| [559] | Emelianova, A.; Nekorkin, V. I., On the intersection of a chaotic attractor and a chaotic repeller in the system of two adaptively coupled phase oscillators, Chaos, 29, 11, Article 111102 pp. (2019) · Zbl 1427.37026 |
| [560] | Emelianova, A. A.; Nekorkin, V. I., The third type of chaos in a system of two adaptively coupled phase oscillators, Chaos, 30, 5, Article 051105 pp. (2020) · Zbl 1437.34042 |
| [561] | Emelianova, A. A.; Nekorkin, V. I., Emergence and synchronization of a reversible core in a system of forced adaptively coupled kuramoto oscillators, Chaos, 31, 3, Article 033102 pp. (2021) · Zbl 1459.34117 |
| [562] | Bačić, I.; Klinshov, V. V.; Nekorkin, V. I.; Perc, M.; Franović, I., Inverse stochastic resonance in a system of excitable active rotators with adaptive coupling, Europhys. Lett., 124, 40004 (2018) |
| [563] | Bačić, I.; Yanchuk, S.; Wolfrum, M.; Franović, I., Noise-induced switching in two adaptively coupled excitable systems, Eur. Phys. J. Spec. Top., 227, 10-11, 1077 (2018) |
| [564] | Bačić, I.; Franović, I., Two paradigmatic scenarios for inverse stochastic resonance, Chaos, 30, 3, Article 033123 pp. (2020) · Zbl 1435.34060 |
| [565] | Franović, I.; Yanchuk, S.; Eydam, S.; Bačić, I.; Wolfrum, M., Dynamics of a stochastic excitable system with slowly adapting feedback, Chaos, 30, 8, Article 083109 pp. (2020) · Zbl 1445.34071 |
| [566] | Madadi Asl, M.; Ramezani Akbarabadi, S., Delay-dependent transitions of phase synchronization and coupling symmetry between neurons shaped by spike-timing-dependent plasticity, Cogn. Neurodyn., 1-14 (2022) |
| [567] | Bick, C.; Goodfellow, M.; Laing, C. R.; Martens, E. A., Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review, J. Math. Neurosci., 10, 9 (2020) · Zbl 1448.92011 |
| [568] | Pitsik, E.; Makarov, V.; Kirsanov, D.; Frolov, N.; Goremyko, M.; Li, X.; Wang, Z.; Hramov, A.; Boccaletti, S., Inter-layer competition in adaptive multiplex network, New J. Phys., 20, 7, Article 075004 pp. (2018) |
| [569] | Frolov, N. S.; Rakshit, S.; Maksimenko, V. A.; Kirsanov, D.; Ghosh, D.; Hramov, A. E., Coexistence of interdependence and competition in adaptive multilayer network, Chaos Solitons Fractals, 147, Article 110955 pp. (2021) · Zbl 1486.94191 |
| [570] | Kachhvah, A. D.; Jalan, S., Hebbian plasticity rules abrupt desynchronization in pure simplicial complexes, New J. Phys., 24, 5, Article 052002 pp. (2022) |
| [571] | Kachhvah, A. D.; Jalan, S., First-order route to antiphase clustering in adaptive simplicial complexes, Phys. Rev. E, 105, 6, L062203 (2022) |
| [572] | Rajwani, P.; Suman, A.; Jalan, S., Tiered synchronization in adaptive kuramoto oscillators on simplicial complexes (2023), arXiv preprint arXiv:2302.12076 |
| [573] | Timme, M., Revealing network connectivity from response dynamics, Phys. Rev. Lett., 98, 22, Article 224101 pp. (2007) |
| [574] | Timme, M.; Casadiego, J., Revealing networks from dynamics: an introduction, J. Phys. A, 47, 34, Article 343001 pp. (2014) · Zbl 1305.92036 |
| [575] | Peixoto, T. P., Network reconstruction and community detection from dynamics, Phys. Rev. Lett., 123, 12, Article 128301 pp. (2019) |
| [576] | Yu, D.; Righero, M.; Kocarev, L., Estimating topology of networks, Phys. Rev. Lett., 97, Article 188701 pp. (2006) |
| [577] | Sawicki, J.; Berner, R.; Loos, S. A.; Anvari, M.; Bader, R.; Barfuss, W.; Botta, N.; Brede, N.; Franović, I.; Gauthier, D. J.; Goldt, S.; Hajizadeh, A.; Hövel, P.; Karin, O.; Lorenz-Spreen, P.; Miehl, C.; Mölter, J.; Olmi, S.; Schöll, E.; Seif, A.; Tass, P. A.; Volpe, G.; Yanchuk, S.; Kurths, J., Perspectives on adaptive dynamical systems, Chaos, 33, 7, Article 071501 pp. (2023) |
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