[1] |
Kuramoto, Y., Chemical Oscillations, Waves and Turbulence, 1984, Springer · Zbl 0558.76051 |
[2] |
Strogatz, S. H., From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators, Physica D, 143, 1-20, 2000 · Zbl 0956.00057 · doi:10.1016/S0167-2789(00)00094-4 |
[3] |
Acebrón, J. A.; Bonilla, L. L.; Vicente, C. J. P.; Ritort, F.; Spigler, R., The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys., 77, 137, 2005 · doi:10.1103/RevModPhys.77.137 |
[4] |
Gupta, S.; Campa, A.; Ruffo, S., Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects, J. Stat. Mech., R08001, 2014 · Zbl 1456.34060 |
[5] |
Rodrigues, F. A.; Peron, T. K. D.; Ji, P.; Kurths, J., The Kuramoto model in complex networks, Phys. Rep., 610, 1-98, 2016 · Zbl 1357.34089 · doi:10.1016/j.physrep.2015.10.008 |
[6] |
Gupta, S.; Campa, A.; Ruffo, S., Statistical Physics of Synchronization, 2018, Springer · Zbl 1407.82003 |
[7] |
Pikovsky, A.; Kurths, J.; Rosenblum, M.; Kurths, J., Synchronization: A Universal Concept in Nonlinear Sciences, 2003, Cambridge University Press · Zbl 1219.37002 |
[8] |
Strogatz, S., Sync: The Emerging Science of Spontaneous Order, 2004, Penguin |
[9] |
Pikovsky, A.; Rosenblum, M., Dynamics of globally coupled oscillators: Progress and perspectives, Chaos, 25, 097616, 2015 · Zbl 1374.34001 · doi:10.1063/1.4922971 |
[10] |
Martens, E. A.; Barreto, E.; Strogatz, S. H.; Ott, E.; So, P.; Antonsen, T. M., Exact results for the Kuramoto model with a bimodal frequency distribution, Phys. Rev. E, 79, 026204, 2009 · doi:10.1103/PhysRevE.79.026204 |
[11] |
Campa, A., Phase diagram of noisy systems of coupled oscillators with a bimodal frequency distribution, J. Phys. A: Math. Theor., 53, 154001, 2020 · Zbl 1514.82155 · doi:10.1088/1751-8121/ab79f2 |
[12] |
Einstein, A., Investigations on the Theory of the Brownian Movement, 1956, Courier Corporation · Zbl 0071.41205 |
[13] |
Majumdar, S. N., “Brownian functionals in physics and computer science,” in The Legacy Of Albert Einstein: A Collection of Essays in Celebration of the Year of Physics (World Scientific, 2007), pp. 93-129. · Zbl 1136.01013 |
[14] |
Mörters, P.; Peres, Y., Brownian Motion, 2010, Cambridge University Press · Zbl 1243.60002 |
[15] |
Evans, M. R.; Majumdar, S. N., Diffusion with stochastic resetting, Phys. Rev. Lett., 106, 160601, 2011 · doi:10.1103/PhysRevLett.106.160601 |
[16] |
Livi, R.; Politi, P., Nonequilibrium Statistical Physics: A Modern Perspective, 2017, Cambridge University Press · Zbl 1451.82001 |
[17] |
Mukamel, D., “Phase transitions in non-equilibrium systems,” cond-mat/0003424 (2000). |
[18] |
Pal, A., Diffusion in a potential landscape with stochastic resetting, Phys. Rev. E, 91, 012113, 2015 · doi:10.1103/PhysRevE.91.012113 |
[19] |
Nagar, A.; Gupta, S., Diffusion with stochastic resetting at power-law times, Phys. Rev. E, 93, 060102, 2016 · doi:10.1103/PhysRevE.93.060102 |
[20] |
Majumdar, S. N.; Oshanin, G., Spectral content of fractional Brownian motion with stochastic reset, J. Phys. A: Math. Theor., 51, 435001, 2018 · Zbl 1407.60056 · doi:10.1088/1751-8121/aadef0 |
[21] |
Den Hollander, F.; Majumdar, S. N.; Meylahn, J. M.; Touchette, H., Properties of additive functionals of Brownian motion with resetting, J. Phys. A: Math. Theor., 52, 175001, 2019 · Zbl 1509.60142 · doi:10.1088/1751-8121/ab0efd |
[22] |
Chatterjee, A.; Christou, C.; Schadschneider, A., Diffusion with resetting inside a circle, Phys. Rev. E, 97, 062106, 2018 · doi:10.1103/PhysRevE.97.062106 |
[23] |
Masoliver, J., Telegraphic processes with stochastic resetting, Phys. Rev. E, 99, 012121, 2019 · doi:10.1103/PhysRevE.99.012121 |
[24] |
Ray, S.; Reuveni, S., Diffusion with resetting in a logarithmic potential, J. Chem. Phys., 152, 234110, 2020 · doi:10.1063/5.0010549 |
[25] |
Montero, M.; Villarroel, J., Directed random walk with random restarts: The Sisyphus random walk, Phys. Rev. E, 94, 032132, 2016 · doi:10.1103/PhysRevE.94.032132 |
[26] |
Méndez, V.; Campos, D., Characterization of stationary states in random walks with stochastic resetting, Phys. Rev. E, 93, 022106, 2016 · doi:10.1103/PhysRevE.93.022106 |
[27] |
Kusmierz, L.; Majumdar, S. N.; Sabhapandit, S.; Schehr, G., First order transition for the optimal search time of Lévy flights with resetting, Phys. Rev. Lett., 113, 220602, 2014 · doi:10.1103/PhysRevLett.113.220602 |
[28] |
Belan, S., Restart could optimize the probability of success in a Bernoulli trial, Phys. Rev. Lett., 120, 080601, 2018 · doi:10.1103/PhysRevLett.120.080601 |
[29] |
Coghi, F.; Harris, R. J., A large deviation perspective on ratio observables in reset processes: Robustness of rate functions, J. Stat. Phys., 179, 131-154, 2020 · Zbl 1437.60016 · doi:10.1007/s10955-020-02513-3 |
[30] |
Kumar, V.; Sadekar, O.; Basu, U., Active Brownian motion in two dimensions under stochastic resetting, Phys. Rev. E, 102, 052129, 2020 · doi:10.1103/PhysRevE.102.052129 |
[31] |
Bressloff, P. C., Modeling active cellular transport as a directed search process with stochastic resetting and delays, J. Phys. A: Math. Theor., 53, 355001, 2020 · Zbl 1519.92062 · doi:10.1088/1751-8121/ab9fb7 |
[32] |
Evans, M. R.; Majumdar, S. N.; Mallick, K., Optimal diffusive search: Nonequilibrium resetting versus equilibrium dynamics, J. Phys. A: Math. Theor., 46, 185001, 2013 · Zbl 1267.82098 · doi:10.1088/1751-8113/46/18/185001 |
[33] |
Pal, A.; Reuveni, S., First passage under restart, Phys. Rev. Lett., 118, 030603, 2017 · doi:10.1103/PhysRevLett.118.030603 |
[34] |
Falcón-Cortés, A.; Boyer, D.; Giuggioli, L.; Majumdar, S. N., Localization transition induced by learning in random searches, Phys. Rev. Lett., 119, 140603, 2017 · doi:10.1103/PhysRevLett.119.140603 |
[35] |
Chechkin, A.; Sokolov, I., Random search with resetting: A unified renewal approach, Phys. Rev. Lett., 121, 050601, 2018 · doi:10.1103/PhysRevLett.121.050601 |
[36] |
Bhat, U.; De Bacco, C.; Redner, S., Stochastic search with Poisson and deterministic resetting, J. Stat. Mech., 2016, 083401, 2016 · Zbl 1456.60235 · doi:10.1088/1742-5468/2016/08/083401 |
[37] |
Ahmad, S.; Nayak, I.; Bansal, A.; Nandi, A.; Das, D., First passage of a particle in a potential under stochastic resetting: A vanishing transition of optimal resetting rate, Phys. Rev. E, 99, 022130, 2019 · doi:10.1103/PhysRevE.99.022130 |
[38] |
Roldán, É.; Lisica, A.; Sánchez-Taltavull, D.; Grill, S. W., Stochastic resetting in backtrack recovery by RNA polymerases, Phys. Rev. E, 93, 062411, 2016 · doi:10.1103/PhysRevE.93.062411 |
[39] |
Tucci, G.; Gambassi, A.; Gupta, S.; Roldán, É., Controlling particle currents with evaporation and resetting from an interval, Phys. Rev. Res., 2, 043138, 2020 · doi:10.1103/PhysRevResearch.2.043138 |
[40] |
Reuveni, S., Optimal stochastic restart renders fluctuations in first passage times universal, Phys. Rev. Lett., 116, 170601, 2016 · doi:10.1103/PhysRevLett.116.170601 |
[41] |
Boyer, D.; Solis-Salas, C., Random walks with preferential relocations to places visited in the past and their application to biology, Phys. Rev. Lett., 112, 240601, 2014 · doi:10.1103/PhysRevLett.112.240601 |
[42] |
Giuggioli, L.; Gupta, S.; Chase, M., Comparison of two models of tethered motion, J. Phys. A: Math. Theor., 52, 075001, 2019 · Zbl 1505.82049 · doi:10.1088/1751-8121/aaf8cc |
[43] |
Gupta, S.; Majumdar, S. N.; Schehr, G., Fluctuating interfaces subject to stochastic resetting, Phys. Rev. Lett., 112, 220601, 2014 · doi:10.1103/PhysRevLett.112.220601 |
[44] |
Gupta, S.; Nagar, A., Resetting of fluctuating interfaces at power-law times, J. Phys. A: Math. Theor., 49, 445001, 2016 · Zbl 1357.82045 · doi:10.1088/1751-8113/49/44/445001 |
[45] |
Durang, X.; Henkel, M.; Park, H., The statistical mechanics of the coagulation-diffusion process with a stochastic reset, J. Phys. A: Math. Theor., 47, 045002, 2014 · Zbl 1293.82016 · doi:10.1088/1751-8113/47/4/045002 |
[46] |
Magoni, M.; Majumdar, S. N.; Schehr, G., Ising model with stochastic resetting, Phys. Rev. Res., 2, 033182, 2020 · doi:10.1103/PhysRevResearch.2.033182 |
[47] |
Basu, U.; Kundu, A.; Pal, A., Symmetric exclusion process under stochastic resetting, Phys. Rev. E, 100, 032136, 2019 · doi:10.1103/PhysRevE.100.032136 |
[48] |
Karthika, S.; Nagar, A., Totally asymmetric simple exclusion process with resetting, J. Phys. A: Math. Theor., 53, 115003, 2020 · Zbl 1514.82131 · doi:10.1088/1751-8121/ab6aef |
[49] |
Fuchs, J.; Goldt, S.; Seifert, U., Stochastic thermodynamics of resetting, Europhys. Lett., 113, 60009, 2016 · doi:10.1209/0295-5075/113/60009 |
[50] |
Mukherjee, B.; Sengupta, K.; Majumdar, S. N., Quantum dynamics with stochastic reset, Phys. Rev. B, 98, 104309, 2018 · doi:10.1103/PhysRevB.98.104309 |
[51] |
Abeles, M., Local Circuits: An Electrophysiological Study (Springer-Verlag, Berlin, 1982). |
[52] |
Ray, A.; Pal, A.; Ghosh, D.; Dana, S. K.; Hens, C., Mitigating long transient time in deterministic systems by resetting, Chaos, 31, 011103, 2021 · Zbl 1466.37060 · doi:10.1063/5.0038374 |
[53] |
Ott, E.; Antonsen, T. M., Low dimensional behavior of large systems of globally coupled oscillators, Chaos, 18, 037113, 2008 · Zbl 1309.34058 · doi:10.1063/1.2930766 |
[54] |
Ott, E.; Antonsen, T. M., Long time evolution of phase oscillator systems, Chaos, 19, 023117, 2009 · Zbl 1309.34059 · doi:10.1063/1.3136851 |
[55] |
Métivier, D.; Gupta, S., Bifurcations in the time-delayed Kuramoto model of coupled oscillators: Exact results, J. Stat. Phys., 176, 279-298, 2019 · Zbl 1448.34075 · doi:10.1007/s10955-019-02299-z |
[56] |
Pazó, D.; Gallego, R., The Winfree model with non-infinitesimal phase-response curve: Ott-Antonsen theory, Chaos, 30, 073139, 2020 · Zbl 1445.34059 · doi:10.1063/5.0015131 |
[57] |
Tanaka, T., Low-dimensional dynamics of phase oscillators driven by Cauchy noise, Phys. Rev. E, 102, 042220, 2020 · doi:10.1103/PhysRevE.102.042220 |
[58] |
Xu, C.; Wang, X.; Skardal, P. S., Universal scaling and phase transitions of coupled phase oscillator populations, Phys. Rev. E, 102, 042310, 2020 · doi:10.1103/PhysRevE.102.042310 |
[59] |
Dai, X.; Li, X.; Guo, H.; Jia, D.; Perc, M.; Manshour, P.; Wang, Z.; Boccaletti, S., Discontinuous transitions and rhythmic states in the D-dimensional Kuramoto model induced by a positive feedback with the global order parameter, Phys. Rev. Lett., 125, 194101, 2020 · doi:10.1103/PhysRevLett.125.194101 |
[60] |
Lipton, M.; Mirollo, R.; Strogatz, S. H., The Kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry, Chaos, 31, 093113, 2021 · Zbl 07866706 · doi:10.1063/5.0060233 |
[61] |
Chandrasekar, V. K.; Manoranjani, M.; Gupta, S., The Kuramoto model in presence of additional interactions that break rotational symmetry, Phys. Rev. E, 102, 012206, 2020 · doi:10.1103/PhysRevE.102.0 |
[62] |
Berner, R.; Yanchuk, S.; Maistrenko, Y.; Schöll, E., Generalized splay states in phase oscillator networks, Chaos, 31, 073128, 2021 · Zbl 1468.34042 · doi:10.1063/5.0056664 |
[63] |
Lucchetti, A.; Jensen, M. H.; Heltberg, M. L., Emergence of chimera states in a neuronal model of delayed oscillators, Phys. Rev. Res., 3, 033041, 2021 · doi:10.1103/PhysRevResearch.3.033041 |
[64] |
Kumarasamy, S.; Dudkowski, D.; Prasad, A.; Kapitaniak, T., Ordered slow and fast dynamics of unsynchronized coupled phase oscillators, Chaos, 31, 081102, 2021 · Zbl 07866657 · doi:10.1063/5.0063513 |
[65] |
Ciszak, M.; Olmi, S.; Innocenti, G.; Torcini, A.; Marino, F., Collective canard explosions of globally-coupled rotators with adaptive coupling, Chaos Soliton. Fract., 153, 111592, 2021 · doi:10.1016/j.chaos.2021.111592 |
[66] |
Laing, C. R., Interpolating between bumps and chimeras, Chaos, 31, 113116, 2021 · Zbl 07871539 · doi:10.1063/5.0070341 |
[67] |
Manoranjani, M.; Gupta, S.; Chandrasekar, V., The Sakaguchi-Kuramoto model in presence of asymmetric interactions that break phase-shift symmetry, Chaos, 31, 083130, 2021 · Zbl 07866688 · doi:10.1063/5.0055664 |
[68] |
Clusella, P.; Pietras, B.; Montbrió, E., Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling, Chaos, 32, 013105, 2022 · Zbl 07867647 · doi:10.1063/5.0075285 |
[69] |
Pikovsky, A., Hierarchy of exact low-dimensional reductions for populations of coupled oscillators, Phys. Rev. Lett., 128, 054101, 2022 · doi:10.1103/PhysRevLett.128.054101 |
[70] |
Omel’chenko, O., Mathematical framework for breathing chimera states, J. Nonlin. Sci., 32, 1-34, 2022 · Zbl 1479.82025 · doi:10.1007/s00332-021-09760-y |
[71] |
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, 1-43, 2020 · Zbl 1448.92011 · doi:10.1186/s13408-020-00086-9 |
[72] |
Strogatz, S. H., Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 2014, Westview Press |
[73] |
Miron, A.; Reuveni, S., Diffusion with local resetting and exclusion, Phys. Rev. Res., 3, L012023, 2021 · doi:10.1103/PhysRevResearch.3.L012023 |
[74] |
Kalos, M. H.; Whitlock, P. A., Monte Carlo Methods, 2009, John Wiley & Sons |