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2013
Impact Factor

Galina Strelkova

Astrakhanskaya st., 83, Saratov, 410012 Russia
Saratov State University

Publications:

Strelkova G. I., Vadivasova T. E., Anishchenko V. S.
Synchronization of Chimera States in a Network of Many Unidirectionally Coupled Layers of Discrete Maps
2018, vol. 23, no. 7-8, pp.  948-960
Abstract
We study numerically external synchronization of chimera states in a network of many unidirectionally coupled layers, each representing a ring of nonlocally coupled discretetime systems. The dynamics of each element in the network is described by either the logistic map or the bistable cubic map. We consider two cases: when all $M$ unidirectionally coupled layers are identical and when $(M - 1)$ identical layers differ from the first driving layer in their nonlocal coupling parameters. It is shown that the master chimera state in the first layer can be retranslating along the network with small distortions which are defined by a parameter mismatch. We also analyze the dependence of the mean-square deviation of the structure in the ith layer on the nonlocal coupling parameters.
Keywords: synchronization, many layer network, chimera states, nonlocal coupling, unidirectional coupling
Citation: Strelkova G. I., Vadivasova T. E., Anishchenko V. S.,  Synchronization of Chimera States in a Network of Many Unidirectionally Coupled Layers of Discrete Maps, Regular and Chaotic Dynamics, 2018, vol. 23, no. 7-8, pp. 948-960
DOI:10.1134/S1560354718070092
Semenova N. I., Rybalova E. V., Strelkova G. I., Anishchenko V. S.
“Coherence–incoherence” Transition in Ensembles of Nonlocally Coupled Chaotic Oscillators with Nonhyperbolic and Hyperbolic Attractors
2017, vol. 22, no. 2, pp.  148-162
Abstract
We consider in detail similarities and differences of the “coherence–incoherence” transition in ensembles of nonlocally coupled chaotic discrete-time systems with nonhyperbolic and hyperbolic attractors. As basic models we employ the Hénon map and the Lozi map. We show that phase and amplitude chimera states appear in a ring of coupled Hénon maps, while no chimeras are observed in an ensemble of coupled Lozi maps. In the latter, the transition to spatio-temporal chaos occurs via solitary states. We present numerical results for the coupling function which describes the impact of neighboring oscillators on each partial element of an ensemble with nonlocal coupling. Varying the coupling strength we analyze the evolution of the coupling function and discuss in detail its role in the “coherence–incoherence” transition in the ensembles of Hénon and Lozi maps.
Keywords: ensemble of nonlocally coupled oscillators, chimera states, solitary states, hyperbolic and nonhyperbolic attractors, coupling function
Citation: Semenova N. I., Rybalova E. V., Strelkova G. I., Anishchenko V. S.,  “Coherence–incoherence” Transition in Ensembles of Nonlocally Coupled Chaotic Oscillators with Nonhyperbolic and Hyperbolic Attractors, Regular and Chaotic Dynamics, 2017, vol. 22, no. 2, pp. 148-162
DOI:10.1134/S1560354717020046

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