Spiral wave chimeras in reaction-diffusion systems: phenomenon, mechanism and transitions. (English) Zbl 1464.35016
Summary: Spiral wave chimeras (SWCs), which combine the features of spiral waves and chimera states, are a new type of dynamical patterns emerged in spatiotemporal systems due to the spontaneous symmetry breaking of the system dynamics. In generating SWC, the conventional wisdom is that the dynamical elements should be coupled in a nonlocal fashion. For this reason, it is commonly believed that SWC is excluded from the general reaction-diffusion (RD) systems possessing only local couplings. Here, by an experimentally feasible model of a three-component FitzHugh-Nagumo-type RD system, we demonstrate that, even though the system elements are locally coupled, stable SWCs can still be observed in a wide region in the parameter space. The properties of SWCs are explored, and the underlying mechanisms are analyzed from the point view of coupled oscillators. Transitions from SWC to incoherent states are also investigated, and it is found that SWCs are typically destabilized in two scenarios, namely core breakup and core expansion. The former is characterized by a continuous breakup of the single asynchronous core into a number of small asynchronous cores, whereas the latter is featured by the continuous expansion of the single asynchronous core to the whole space. Remarkably, in the scenario of core expansion, the system may develop into an intriguing state in which regular spiral waves are embedded in a completely disordered background. This state, which is named shadowed spirals, manifests from a new perspective the coexistence of incoherent and coherent states in spatiotemporal systems, generalizing therefore the traditional concept of chimera states. Our studies provide an affirmative answer to the observation of SWCs in typical RD systems, and pave a way to the realization of SWCs in experiments.
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35K57 | Reaction-diffusion equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
References:
| [1] | Kuramoto, Y.; Battogtokh, D., Coexistence of coherence and incoherence in nonlocally coupled phase oscillators, Nonlinear Phenom Complex Syst, 5, 380 (2002) |
| [2] | Abrams, D. M.; Strogatz, S. H., Chimera states for coupled oscillators, Phys Rev Lett, 93, 174102 (2004) |
| [3] | Abrams, D. M.; Mirollo, R.; Strogatz, S. H.; Wiley, D. A., Solvable model for chimera states of coupled oscillators, Phys Rev Lett, 101, 084103 (2008) |
| [4] | Panaggio, M. J.; Abrams, D. M., Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators, Nonlinearity, 28, R67 (2015) · Zbl 1392.34036 |
| [5] | Omel’chenko, O. E.; Maistrenko, Y. L.; Tass, P. A., Chimera states: the natural link between coherence and incoherence, Phys Rev Lett, 100, 044105 (2008) |
| [6] | Sethia, G. C.; Sen, A.; Atay, F. M., Clustered chimera states in delay-coupled oscillator systems, Phys Rev Lett, 100, 144102 (2008) |
| [7] | Omelchenko, I.; Maistrenko, Y.; Hövel, P.; Schöll, E., Loss of coherence in dynamical networks: spatial chaos and chimera states, Phys Rev Lett, 106, 234102 (2011) |
| [8] | Omelchenko, I.; Omel’chenko, O. E.; Hövel, P.; Schöll, E., When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states, Phys Rev Lett, 110, 224101 (2013) |
| [9] | Semenova, N.; Zakharova, A.; Anishchenko, V.; Schöll, E., Coherence-resonance chimeras in a network of excitable elements, Phys Rev Lett, 117, 014102 (2016) |
| [10] | Dai, Q.; Zhang, M.; Cheng, H.; Li, H.; Xie, F.; Yang, J., From collective oscillation to chimera state in a nonlocally coupled excitable system, Nonlinear Dyn, 91, 1723 (2018) |
| [11] | Shepelev, I. A.; Bukh, A. V.; Vadivasova, T. E.; Anishchenko, V. S.; Zakharova, A., Double-well chimeras in 2D lattice of chaotic bistable elements, Commun Nonlinear Sci Numer Simul, 54, 50 (2018) · Zbl 1452.37078 |
| [12] | Laing, C. R., The dynamics of chimera states in heterogeneous Kuramoto networks, Phys D, 238, 1569 (2009) · Zbl 1185.34042 |
| [13] | Wang, W.; Dai, Q.; Cheng, H.; Li, H.; Yang, J., The drift of chimera states in a ring of nonlocally coupled bicomponent phase oscillators, EPL, 125, 50007 (2019) |
| [14] | Dai, Q. L.; Liu, X. X.; Yang, K.; Cheng, H. Y.; Li, H. H.; Xie, F., Entangled chimeras in nonlocally coupled bicomponent phase oscillators: from synchronous to asynchronous chimeras, Front Phys, 15, 62501 (2020) |
| [15] | Gavrilov, S. S., Polariton chimeras: Bose-Einstein condensates with intrinsic chaoticity and spontaneous long range ordering, Phys Rev Lett, 120, 033901 (2018) |
| [16] | Xu, H. Y.; Wang, G. L.; Huang, L.; Lai, Y. C., Chaos in dirac electron optics: emergence of a relativistic quantum chimera, Phys Rev Lett, 120, 124101 (2018) |
| [17] | Hagerstrom, A. M.; Murphy, T. E.; Roy, R.; Hövel, P.; Omelchenko, I.; Schöll, E., Experimental observation of chimeras in coupled-map lattices, Nat Phys, 8, 658 (2012) |
| [18] | Tinsley, M. R.; Nkomo, S.; Showalter, K., Chimera and phase-cluster states in populations of coupled chemical oscillators, Nat Phys, 8, 662 (2012) |
| [19] | Nkomo, S.; Tinsley, M. R.; Showalter, K., Chimera states in populations of nonlocally coupled chemical oscillators, Phys Rev Lett, 110, 244102 (2013) |
| [20] | Martens, E. A.; Thutupalli, S.; Fourriere, A.; Hallatschek, O., Chimera states in mechanical oscillator networks, Proc Natl Acad Sci USA, 110, 10563 (2013) |
| [21] | Gambuzza, L. V.; Buscarino, A.; Chessari, S.; Fortuna, L.; Meucci, R.; Frasca, M., Experimental investigation of chimera states with quiescent and synchronous domains in coupled electronic oscillators, Phys Rev E, 90, 032905 (2014) |
| [22] | Wickramasinghe, M.; Kiss, I. Z., Spatially organized partial synchronization through the chimera mechanism in a network of electrochemical reactions, Phys Chem Chem Phys, 16, 18360 (2014) |
| [23] | Larger, L.; Penkovsky, B.; Maistrenko, Y., Laser chimeras as a paradigm formultistable patterns in complex systems, Nat Commun, 6, 7752 (2015) |
| [24] | Sethia, G. C.; Sen, A., Chimera states: the existence criteria revisited, Phys Rev Lett, 112, 144101 (2014) |
| [25] | Yeldesbay, A.; Pikovsky, A.; Rosenblum, M., Chimeralike states in an ensemble of globally coupled oscillators, Phys Rev Lett, 112, 144103 (2014) |
| [26] | Kemeth, F. P.; Haugland, S. W.; Schmidt, L.; Kevrekidis, I. G.; Krischer, K., A classification scheme for chimera states, Chaos, 26, 094815 (2016) |
| [27] | Laing, C. R., Chimeras in networks with purely local coupling, Phys Rev E, 92, 050904(R) (2015) |
| [28] | Bera, B. K.; Majhi, S.; Ghosh, D.; Perc, M., Chimera states: effects of different coupling topologies, EPL, 118, 10001 (2017) |
| [29] | Tian, C.; Bi, H.; Zhang, X.; Guan, S.; Liu, Z., Asymmetric couplings enhance the transition from chimera state to synchronization, Phys Rev E, 96, 052209 (2017) |
| [30] | Zhu, Y.; Zheng, Z. G.; Yang, J., Reversed two-cluster chimera state in non-locally coupled oscillators with heterogeneous phase lags, EPL, 103, 10007 (2013) |
| [31] | Zakharova, A.; Kapeller, M.; Schöll, E., Chimera death: symmetry breaking in dynamical networks, Phys Rev Lett, 112, 154101 (2014) |
| [32] | Clerc, M. G.; Coulibaly, S.; Ferré, M. A.; Garcìa-Ñustes, M. A.; Rojas, R. G., Chimera-type states induced by local coupling, Phys Rev E, 93, 052204 (2016) |
| [33] | Bera, B. K.; Ghosh, D.; Banerjee, T., Imperfect traveling chimera states induced by local synaptic gradient coupling, Phys Rev E, 94, 012215 (2016) |
| [34] | Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M., Stable amplitude chimera states in a network of locally coupled stuart-landau oscillators, Chaos, 28, 033110 (2018) · Zbl 1390.34148 |
| [35] | Shima, S.; Kuramoto, Y., Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators, Phys Rev E, 69, 036213 (2004) |
| [36] | Martens, E. A.; Laing, C. R.; Strogatz, S. H., Solvable model of spiral wave chimeras, Phys Rev Lett, 104, 044101 (2010) |
| [37] | Bera, B. K.; Ghosh, D., Chimera states in purely local delay-coupled oscillators, Phys Rev E, 93, 052223 (2016) |
| [38] | Kundu, S.; Majhi, S.; Bera, B. K.; Ghosh, D.; Lakshmanan, M., Chimera states in two-dimensional networks of locally coupled oscillators, Phys Rev E, 97, 022201 (2018) |
| [39] | Kundu, S.; Bera, B. K.; Ghosh, D.; Lakshmanan, M., Chimera patterns in three-dimensional locally coupled systems, Phys Rev E, 99, 022204 (2019) |
| [40] | Clerca, M. G.; Coulibaly, S.; Ferré, M. A., Freak chimera states in a locally coupled duffing oscillators chain, Commun Nonlinear Sci Numer Simul, 89, 105288 (2020) · Zbl 1455.34031 |
| [41] | Zhu, Y.; Li, Y.; Zhang, M.; Yang, J., The oscillating two-cluster chimera state in non-locally coupled phase oscillators, EPL, 97, 10009 (2012) |
| [42] | Sethia, G. C.; Sen, A.; Johnston, G. L., Amplitude-mediated chimera states, Phys Rev E, 88, 042917 (2013) |
| [43] | Buscarino, A.; Frasca, M.; Gambuzza, L. V.; Hövel, P., Chimera states in time-varying complex networks, Phys Rev, 91, 022817 (2015) |
| [44] | Xiao, G.; Liu, W.; Lan, Y.; Xiao, J., Stable amplitude chimera states and chimera death in repulsively coupled chaotic oscillators, Nonlinear Dyn, 93, 1047 (2018) |
| [45] | Zhang, Y.; Nicolaou, Z. G.; Hart, J. D.; Roy, R.; Motter, A. E., Critical switching in globally attractive chimeras, Phys Rev X, 10, 011044 (2020) |
| [46] | Alvarez-Socorro, A. J.; Clerc, M. G.; Verschueren, N., Traveling chimera states in continuous media, Commun Nonlinear Sci Numer Simul, 94, 105559 (2021) · Zbl 1455.74010 |
| [47] | Yao, N.; Huang, Z. G.; Lai, Y. C.; Zheng, Z. G., Robustness of chimera states in complex dynamical systems, Sci Rep, 3, 3522 (2013) |
| [48] | Zhu, Y.; Zheng, Z. G.; Yang, J., Chimera states on complex networks, Phys Rev E, 89, 022914 (2014) |
| [49] | Jiang, X.; Abrams, D. M., Symmetry-broken states on networks of coupled oscillators, Phys Rev E, 93, 052202 (2016) |
| [50] | Makarov, V. V.; Kundu, S.; Kirsanov, D. V.; Frolov, N. S.; Maksimenko, V. A.; Ghosh, D.; Dana, S. K.; Hramov, A. E., Multiscale interaction promotes chimera states in complex networks, Commun Nonlinear Sci Numer Simul, 71, 118 (2019) · Zbl 1464.92056 |
| [51] | Majhi, S.; Bera, B. K.; Ghosh, D.; Perc, M., Chimera states in neuronal networks: a review, Phys Life Rev, 28, 100 (2019) |
| [52] | Huo, S.; Tian, C.; Zheng, M.; Guan, S.; Zhou, C. S.; Liu, Z., Spatial multi-scaled chimera states of cerebral cortex network and its inherent structure-dynamics relationship in human brain, Nat Sci Rev, 8, nwaa125 (2021) |
| [53] | Shafiei, M.; Jafari, S.; Parastesh, F.; Ozer, M.; Kapitaniak, T.; Perc, M., Time delayed chemical synapses and synchronization in multilayer neuronal networks with ephaptic inter-layer coupling, Commun Nonlinear Sci Numer Simul, 84, 105175 (2020) · Zbl 1451.92030 |
| [54] | Zheng, Z. G.; Zhai, Y., Chimera state: from complex networks to spatiotemporal patterns, Sci Sin-Phys Mech Astron, 50, 010505 (2020) |
| [55] | Rattenborg, N. C.; Amlaner, C. J.; Lima, S. L., Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep, Neurosci Biobehav Rev, 24, 817 (2000) |
| [56] | Tian, C. H.; Zhang, X. Y.; Wang, Z. H.; Liu, Z. H., Diversity of chimera-like patterns from a model of 2Darrays of neurons with nonlocal coupling, Front Phys, 12, 128904 (2017) |
| [57] | Shepelev, I. A.; Vadivasova, T. E., Variety of spatiotemporal regimes in a 2d lattice of coupled bistable FitzHugh-Nagumo oscillators. Formation mechanisms of spiral and double-well chimeras, Commun Nonlinear Sci Numer Simul, 79, 104925 (2019) · Zbl 1508.92039 |
| [58] | Cross, M.; Greenside, H., Pattern formation and dynamics in nonequilibrium systems (2010), Cambridge University Press: Cambridge University Press Cambridge |
| [59] | Winfree, A. T., Spiral waves of chemical activity, Science, 175, 634 (1972) |
| [60] | Jakubith, S.; Rotermund, H. H.; Engel, W.; von Oertzen, A.; Ertl, G., Spatiotemporal concentration patterns in a surface reaction: propagating and standing waves, rotating spirals, and turbulence, Phys Rev Lett, 65, 3013 (1990) |
| [61] | Morris, S. W.; Bodenschatz, E.; Cannell, D. S.; Ahlers, G., Spiral defect chaos in large aspect ratio Rayleigh-Bénard convection, Phys Rev Lett, 71, 2026 (1993) |
| [62] | Sawai, S.; Thomason, P. A.; Cox, E. C., An autoregulatory circuit for long-range self-organization in Dictyostelium cell populations, Nature, 433, 323 (2005) |
| [63] | Kang, Y.; Chen, Y.; Fu, Y.; Wang, Z.; Chen, G., Formation of spiral wave in Hodgkin-Huxley neuron networks with gamma-distributed synaptic input, Commun Nonlinear Sci Numer Simul, 83, 105112 (2020) · Zbl 1454.34027 |
| [64] | Pertsov, A. M.; Davidenko, J. M.; Salomonsz, R.; Baxter, W. T.; Jalife, J., Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle, Circ Res, 72, 631 (1993) |
| [65] | Li, G.; Ouyang, Q.; Petrov, V.; Swinney, H. L., Transition from simple rotating chemical spirals to meandering and traveling spirals, Phys Rev Lett, 77, 2105 (1996) |
| [66] | Barkley, D., Euclidean symmetry and the dynamics of rotating spiral waves, Phys Rev Lett, 72, 164 (1994) |
| [67] | Bär, M.; Eiswirth, M., Turbulence due to spiral breakup in a continuous excitable medium, Phys Rev E, 48, R1635(R) (1993) |
| [68] | Lacitignola, D.; Sgura, I.; Bozzini, B.; Dobrovolska, T.; Krastev, I., Spiral waves on the sphere for an alloy electrodeposition model, Commun Nonlinear Sci Numer Simul, 79, 104930 (2019) · Zbl 1510.78044 |
| [69] | Li, Y.; Li, H.; Zhu, Y.; Zhang, M.; Yang, J., Type of spiral wave with trapped ions, Phys Rev E, 84, 066212 (2011) |
| [70] | Gu, C.; St-Yves, G.; Davidsen, J., Spiral wave chimeras in complex oscillatory and chaotic systems, Phys Rev Lett, 111, 134101 (2013) |
| [71] | Tang, X.; Yang, T.; Epstein, I. R.; Liu, Y.; Zhao, Y.; Gao, Q., Novel type of chimera spiral waves arising from decoupling of a diffusible component, J Chem Phys, 141, 024110 (2014) |
| [72] | Xie, J.; Knobloch, E.; Kao, H. C., Twisted chimera states and multicore spiral chimera states on a two-dimensional torus, Phys Rev E, 92, 042921 (2015) |
| [73] | Maistrenko, Y.; Sudakov, O.; Osiv, O.; Maistrenko, V., Chimera states in three dimensions, New J Phys, 17, 073037 (2015) |
| [74] | Li, B. W.; Dierckx, H., Spiral wave chimeras in locally coupled oscillator systems, Phys Rev E, 93, 020202(R) (2016) |
| [75] | Nicolaou, Z. G.; Riecke, H.; Motter, A. E., Chimera states in continuous media: existence and distinctness, Phys Rev Lett, 119, 244101 (2017) |
| [76] | Kundu, S.; Majhi, S.; Muruganandam, P.; Ghosh, D., Diffusion induced spiral wave chimeras in ecological system, Eur Phys J Spec Top, 227, 983 (2018) |
| [77] | Omel’chenko, O. E.; Wolfrum, M.; Knobloch, E., Stability of spiral chimera states on a torus, SIAM J Appl Dyn Syst, 17, 97 (2018) · Zbl 1386.37047 |
| [78] | Guo, S.; Dai, Q.; Cheng, H.; Li, H.; Xie, F.; Yang, J., Spiral wave chimera in two-dimensional nonlocally coupled FitzHugh-Nagumo systems, Chaos Solitons Fractals, 114, 394 (2018) · Zbl 1415.34070 |
| [79] | Rybalova, E.; Bukh, A.; Strelkova, G.; Anishchenko, V., Spiral and target wave chimeras in a 2D lattice of map-based neuron models, Chaos, 29, 101104 (2019) · Zbl 1426.37057 |
| [80] | Totz, J. F.; Tinsley, M. R.; Engel, H.; Showalter, K., Transition from spiral wave chimeras to phase cluster states, Sci Rep, 10, 7821 (2020) |
| [81] | Maistrenko, V.; Sudakov, O.; Maistrenko, Y., Spiral wave chimeras for coupled oscillators with inertia, Eur Phys J Spec Top, 229, 2327 (2020) |
| [82] | Totz, J. F.; Rode, J.; Tinsley, M. R.; Showalter, K.; Engel, H., Spiral wave chimera states in large populations of coupled chemical oscillators, Nat Phys, 14, 282 (2018) |
| [83] | Alonso, S.; John, K.; Bär, M., Complex wave patterns in an effective reaction-diffusion model for chemical reactions in microemulsions, J Chem Phys, 134, 094117 (2011) |
| [84] | Nicola, E. M.; Or-Guil, M.; Wolf, W.; Bär, M., Drifting pattern domains in a reaction-diffusion system with nonlocal coupling, Phys Rev E, 65, 055101(R) (2002) |
| [85] | Cherkashin, A. A.; Vanag, V. K.; Epstein, I. R., Discontinuously propagating waves in the bathoferroin-Belousov-Zhabotinsky reaction incorporated into a microemulsion, J Chem Phys, 128, 204508 (2008) |
| [86] | Schenk, C. P.; Or-Guil, M.; Bode, M.; Purwins, H. G., Interacting pulses in three-component reaction-diffusion systems on two-dimensional domains, Phys Rev Lett, 78, 3781 (1997) |
| [87] | Danino, T.; Mondragon-Palomino, O.; Tsimring, L.; Hasty, J., A synchronized quorum of genetic clocks, Nature, 463, 326 (2010) |
| [88] | Cao, X. Z.; He, Y.; Li, B. W., Selection of spatiotemporal patterns in arrays of spatially distributed oscillators indirectly coupled via a diffusive environment, Chaos, 29, 043104 (2019) · Zbl 1412.34154 |
| [89] | Schütze J., Mair T., Hauser M.J.B., Falcke M., Wolf J.. Metabolic synchronization by traveling waves in yeast cell layers. J Biophys, 2011. 100, 809, |
| [90] | Noorbakhsh, J.; Schwab, D. J.; Sgro, A. E.; Gregor, T.; Mehta, P., Modeling oscillations and spiral waves in Dictyostelium populations, Phys Rev E, 91, 062711 (2015) |
| [91] | Aldridge, J.; Pye, E. K., Cell density dependence of oscillatory metabolism, 259, 670 (1976) |
| [92] | Camilli, A.; Bassler, B. L., Bacterial small-molecule signaling pathways, Science, 311, 1113 (2006) |
| [93] | Pikovsky, A. S.; Rosenblum, M.; Kurths, J., Synchronization: a universal concept in nonlinear sciences (2001), Cambridge University Press: Cambridge University Press Cambridge, U. K. · Zbl 0993.37002 |
| [94] | Iyer, A. N.; Gray, R. A., An experimentalist’s approach to accurate localization of phase singularities during reentry, Ann Biomed Eng, 29, 47 (2001) |
| [95] | Li, B. W.; Cao, X. Z.; Fu, C., Quorum sensing in populations of spatially extended chaotic oscillators coupled indirectly via a heterogeneous environment, J Nonlinear Sci, 27, 1667 (2017) · Zbl 1381.34076 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
