Discontinuous coupling and transition from synchronization to an intermittent transient chimera state

Document Type : Article

Authors

1 Shaanxi Engineering Research Center of Controllable Neutron Source, School of Science, Xijing University, Xi'an 710123, P.R. China

2 Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar

3 - Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam. - Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland

4 Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland

10.24200/sci.2021.57386.5212

Abstract

The coexistence of coherent and incoherent clusters, which is named chimera state, has been observed in various coupling configurations. The majority of the studies have considered a static scheme for the network. In this paper, the synchronization patterns of a time-varying network with discontinuous coupling (on/off links) are studied. At first, the prerequisites for the synchronization of continuous and discontinuous coupling are found by the master stability function method. It is observed that when the network with continuous coupling is set in the synchronous region, changing the coupling to a discontinuous one leads to the emergence of a pattern consisting of alternating synchronization, asynchronization, and chimera state. We call this pattern intermittent transient chimera. The study is completed by investigating the effect of the rate of discontinuity on the network behavior.

Keywords


References:
[1] Boccaletti S, Kurths J, Osipov G, et al. The synchronization of chaotic systems. Phys Rep. 2002;366:1-101.
[2] Majhi S, Ghosh D. Synchronization of moving oscillators in three dimensional space. Chaos. 2017;27:053115.
[3] Pecora LM, Carroll TL. Synchronization of chaotic systems. Chaos. 2015;25:097611.
[4] Zhang X, Boccaletti S, Guan S, et al. Explosive synchronization in adaptive and multilayer networks. Phys Rev Lett. 2015;114:038701.
[5] Panaggio MJ, Abrams DM. Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators. Nonlinearity. 2015;28:R67.
[6] Abrams DM, Strogatz SH. Chimera states for coupled oscillators. Phys Rev Lett. 2004;93:174102.
[7] Parastesh F, Jafari S, Azarnoush H, et al. Chimeras. Phys Rep. 2020:In Press.
[8] Kuramoto Y, Battogtokh D. Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Nonl Phen Compl Syst. 2002;5:380-5.
[9] Majhi S, Perc M, Ghosh D. Chimera states in a multilayer network of coupled and uncoupled neurons. Chaos. 2017;27:073109.
[10] Omelchenko I, Provata A, Hizanidis J, et al. Robustness of chimera states for coupled FitzHugh-Nagumo oscillators. Phys Rev E. 2015;91:022917.
[11] Wei Z, Parastesh F, Azarnoush H, et al. Nonstationary chimeras in a neuronal network. EPL (Europhys Lett). 2018;123:48003.
[12] Chouzouris T, Omelchenko I, Zakharova A, et al. Chimera states in brain networks: Empirical neural vs. modular fractal connectivity. Chaos. 2018;28:045112.
[13] Loos SA, Claussen JC, Schöll E, et al. Chimera patterns under the impact of noise. Phys Rev E. 2016;93:012209.
[14] Dudkowski D, Maistrenko Y, Kapitaniak T. Occurrence and stability of chimera states in coupled externally excited oscillators. Chaos. 2016;26:116306.
[15] Parastesh F, Chen C-Y, Azarnoush H, et al. Synchronization patterns in a blinking multilayer neuronal network. Eur Phys J Spec Top. 2019;228:2465-74.
[16] Wang Z, Baruni S, Parastesh F, et al. Chimeras in an adaptive neuronal network with burst-timing-dependent plasticity. Neurocomputing. 2020;406:117-26.
[17] Parastesh F, Jafari S, Azarnoush H, et al. Chimera in a network of memristor-based Hopfield neural network. Eur Phys J Spec Top. 2019;228:2023-33.
[18] Khaleghi L, Panahi S, Chowdhury SN, et al. Chimera states in a ring of map-based neurons. Physica A. 2019;536:122596.
[19] Hagerstrom AM, Murphy TE, Roy R, et al. Experimental observation of chimeras in coupled-map lattices. Nature Phys. 2012;8:658.
[20] Nkomo S, Tinsley MR, Showalter K. Chimera states in populations of nonlocally coupled chemical oscillators. Phys Rev Lett. 2013;110:244102.
[21] Awal NM, Bullara D, Epstein IR. The smallest chimera: Periodicity and chaos in a pair of coupled chemical oscillators. Chaos. 2019;29:013131.
[22] Dudkowski D, Grabski J, Wojewoda J, et al. Experimental multistable states for small network of coupled pendula. Sci Rep. 2016;6:29833.
[23] Dudkowski D, Czołczyński K, Kapitaniak T. Traveling chimera states for coupled pendula. Nonlinear Dyn. 2019;95:1859-66.
[24] Carvalho PR, Savi MA. Synchronization and chimera state in a mechanical system. Nonlinear Dyn. 2020;102: 907–925.
[25] Gambuzza LV, Buscarino A, Chessari S,et al. Experimental investigation of chimera states with quiescent and synchronous domains in coupled electronic oscillators. Phys Rev E. 2014;90:032905.
[26] Majhi S, Bera BK, Ghosh D, et al. Chimera states in neuronal networks: A review. Phys Life Rev. 2019;28:100-21.
[27] Bao H, Zhang Y, Liu W, et al. Memristor synapse-coupled memristive neuron network: synchronization transition and occurrence of chimera. Nonlinear Dyn. 2020;100:937–50.
[28] Andreev AV, Ivanchenko MV, Pisarchik AN, et al. Stimulus classification using chimera-like states in a spiking neural network. Chaos, Solitons & Fractals. 2020;139:110061.
[29] Wang S, He S, Rajagopal K, Karthikeyan A, et al. Route to hyperchaos and chimera states in a network of modified Hindmarsh-Rose neuron model with electromagnetic flux and external excitation. Euro Phys J Spec Top. 2020;229:929-42.
[30] Ruzzene G, Omelchenko I, Sawicki J, et al. Remote pacemaker control of chimera states in multilayer networks of neurons. Phys Rev E. 2020;102:052216.
[31] Bansal K, Garcia JO, Tompson SH, et al. Cognitive chimera states in human brain networks. Sci Adv. 2019;5:eaau8535.
[32] Bera BK, Ghosh D. Chimera states in purely local delay-coupled oscillators. Phys Rev E. 2016;93:052223.
[33] Yeldesbay A, Pikovsky A, Rosenblum M. Chimeralike states in an ensemble of globally coupled oscillators. Phys Rev Lett. 2014;112:144103.
[34] Clerc M, Coulibaly S, Ferré M, et al. Chimera-type states induced by local coupling. Phys Rev E. 2016;93:052204.
[35] Schmidt L, Krischer K. Clustering as a prerequisite for chimera states in globally coupled systems. Phys Rev Lett. 2015;114:034101.
[36] Buscarino A, Frasca M, Gambuzza LV, et al. Chimera states in time-varying complex networks. Phys Rev E. 2015;91:022817.
[37] Kasatkin D, Yanchuk S, Schöll E, et al. Self-organized emergence of multilayer structure and chimera states in dynamical networks with adaptive couplings. Phys Rev E. 2017;96:062211.
[38] Kasatkin D, Nekorkin V. Synchronization of chimera states in a multiplex system of phase oscillators with adaptive couplings. Chaos. 2018;28:093115.
[39] Huo S, Tian C, Kang L, et al. Chimera states of neuron networks with adaptive coupling. Nonlinear Dyn. 2019;96:75-86.
[40] Bera BK, Ghosh D, Banerjee T. Imperfect traveling chimera states induced by local synaptic gradient coupling. Phys Rev E. 2016;94:012215.
[41] Omelchenko I, Omel’chenko E, Hövel P, et al. When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states. Phys Rev Lett. 2013;110:224101.
[42] Kundu S, Bera BK, Ghosh D, et al. Chimera patterns in three-dimensional locally coupled systems. Phys Rev E. 2019;99:022204.
[43] Pecora LM, Carroll TL. Master stability functions for synchronized coupled systems. Phys Rev Lett. 1998;80:2109.