Forced synchronization of a multilayer heterogeneous network of chaotic maps in the chimera state mode

Rybalova, Elena; Вадивасова, Т. Е.; Strelkova, Galina I.; Анищенко, В. С.; Zakharova, Anna

doi:10.1063/1.5090184

Cited by 52 publications

(22 citation statements)

References 25 publications

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“…The first experimental observation of chimeras in electro-optical coupled map lattices in one and two dimensions was provided by Hagerstrom et al 24 Apart from coupled logistic maps, 22,23,[27][28][29][30][37][38][39][41][42][43][44] chimera states were illustrated for coupled Henon maps, 26,[32][33][34]36 sinecircle maps, 45,46 sine-squared maps, 35,44 cosine maps, 24 piecewise linear and logistic maps, 25 and cubic maps. 31,39,40 They were found for ring networks with nonlocal coupling, [22][23][24][25][26][28][29][30][31][32][33][34][35][36]39,[41][42][43] ring networks with hierarchical connectivity, 38 globally coupled networks with delay, …”

Section: Articlementioning

confidence: 99%

“…31,39,40 They were found for ring networks with nonlocal coupling, [22][23][24][25][26][28][29][30][31][32][33][34][35][36]39,[41][42][43] ring networks with hierarchical connectivity, 38 globally coupled networks with delay, 35 two-dimensional lattices, 24,40 as well as two-, 27,34,37 three-, 43 and many-layer multiplex networks. 39,41 Apart from phase chimeras, [22][23][24][28][29][30][31][32][33][34]36,[38][39][40][41][42][43] the existence of amplitude chimeras, [28][29]…”

Section: Articlementioning

confidence: 99%

See 1 more Smart Citation

Two populations of coupled quadratic maps exhibit a plentitude of symmetric and symmetry broken dynamics

Andrzejak

Ruzzene

Schöll

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We numerically study a network of two identical populations of identical real-valued quadratic maps. Upon variation of the coupling strengths within and across populations, the network exhibits a rich variety of distinct dynamics. The maps in individual populations can be synchronized or desynchronized. Their temporal evolution can be periodic or aperiodic. Furthermore, one can find blends of synchronized with desynchronized states and periodic with aperiodic motions. We show symmetric patterns for which both populations have the same type of dynamics as well as chimera states of a broken symmetry. The network can furthermore show multistability by settling to distinct dynamics for different realizations of random initial conditions or by switching intermittently between distinct dynamics for the same realization. We conclude that our system of two populations of a particularly simple map is the most simple system that can show this highly diverse and complex behavior, which includes but is not limited to chimera states. As an outlook to future studies, we explore the stability of two populations of quadratic maps with a complex-valued control parameter. We show that bounded and diverging dynamics are separated by fractal boundaries in the complex plane of this control parameter.

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Section: Articlementioning

confidence: 99%

Section: Articlementioning

confidence: 99%

Two populations of coupled quadratic maps exhibit a plentitude of symmetric and symmetry broken dynamics

Andrzejak

Ruzzene

Schöll

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…Synchronization is one of important and fundamental phenomena of self-organization of nonlinear self-oscillating systems [1][2][3][4][5][6]. Recently, there has been great interest in the study of the dynamics of interconnected complex ensembles and networks and, in particular, various forms of synchronization: cluster [7,8], generalized [9], relay [10][11][12][13][14], forced and mutual [15][16][17][18][19][20][21][22], intralayer and interlayer [23][24][25][26], and explosive synchronization [27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Peculiarities of Synchronization in a Two-Layer Network of Chaotic Maps with Inhomogeneous Interlayer Coupling

Bogatenko¹,

Bukh²,

Strelkova³

2021

Nelin. Dinam.

Self Cite

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This paper considers the effects of forced and mutual synchronization of complex spatio-temporal structures in a two-layer network of nonlocally coupled logistic maps in the presence of inhomogeneous interlayer coupling. Two different types of coupling topology are considered: the first one is the sparse interlayer coupling with randomly distributed coupling defects, and the second type is the cluster interlayer coupling, providing the coupling via designated finite groups of elements. The latter type of coupling topology is considered for the first time. As a quantitative measure of the synchronization effect on the network, variance averaged over time and variance averaged both over time and network elements are used. We analyze how the synchronization measure changes depending on a degree of the interlayer coupling sparseness. We also identify a cluster of network elements which can provide almost complete synchronization in the network under study when the interlayer coupling is introduced along them.

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“…Of particular interest is the synchronization of chimera states in multicomponent systems and networks. Recently, various synchronization scenarios in multiplex and multilayer [23][24][25][26][27][28][29][30][31] networks were studied, such as generalized synchronization [32], inter-layer (external and mutual) synchronization [33][34][35][36][37][38], relay (remote) synchronization [39,40], explosive synchronization [41][42][43][44]. Among a large variety of chimera states [35,, here we concentrate on so-called "spiral wave chimera structures" which are observed in 2D ensembles of coupled nonlinear oscillators [10,22,[73][74][75][76][77][78][79][80][81][82][83][84][85][86].…”

Section: Introductionmentioning

confidence: 99%

Spiral Wave Patterns in Two-Layer 2D Lattices of Nonlocally Coupled Discrete Oscillators. Synchronization of Spiral Wave Chimeras

Bukh¹,

Strelkova²,

Анищенко³

2019

ISUNSSP

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The paper describes the spatio-temporal dynamics of a lattice that is given by a 2D N × N network of nonlocally coupled Nekorkin maps which model neuronal activity. The network behavior is studied for periodic and no-flux boundary conditions. It is shown that for certain values of the coupling parameters, rotating spiral waves and spiral wave chimeras can be observed in the considered lattice. We analyze and compare statistical and dynamical characteristics of the local oscillators from coherence and incoherence clusters of a spiral wave chimera. Furthermore, effects of mutual and external synchronization of spiral wave structures in two coupled such lattices are studied. We show numerically that spiral wave structures, including spiral wave chimeras, can be synchronized and establish the mechanism of their synchronization. Our numerical studies indicate that when the coupling strength between the lattices is sufficiently weak, only a certain part of oscillators of the interacting networks is imperfectly synchronized, while the other part demonstrates a partially synchronous behavior. If the spatiotemporal patterns in the lattices do not include incoherent cores, imperfect synchronization is realized for most oscillators above a certain value of the coupling strength. In the regime of spiral wave chimeras, the imperfect synchronization of all oscillators cannot be achieved even for sufficiently large values of the coupling strength.

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Forced synchronization of a multilayer heterogeneous network of chaotic maps in the chimera state mode

Cited by 52 publications

References 25 publications

Two populations of coupled quadratic maps exhibit a plentitude of symmetric and symmetry broken dynamics

Two populations of coupled quadratic maps exhibit a plentitude of symmetric and symmetry broken dynamics

Peculiarities of Synchronization in a Two-Layer Network of Chaotic Maps with Inhomogeneous Interlayer Coupling

Spiral Wave Patterns in Two-Layer 2D Lattices of Nonlocally Coupled Discrete Oscillators. Synchronization of Spiral Wave Chimeras

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