Astrakhanskaya str., 83 410026, Saratov, Russia
Saratov State University
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
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.
Bukh A. V., Slepnev A. V., Anishchenko V. S., Vadivasova T. E.
Stability and Noise-induced Transitions in an Ensemble of Nonlocally Coupled Chaotic Maps
2018, vol. 23, no. 3, pp. 325-338
The influence of noise on chimera states arising in ensembles of nonlocally coupled chaotic maps is studied. There are two types of chimera structures that can be obtained in such ensembles: phase and amplitude chimera states. In this work, a series of numerical experiments is carried out to uncover the impact of noise on both types of chimeras. The noise influence on a chimera state in the regime of periodic dynamics results in the transition to chaotic dynamics. At the same time, the transformation of incoherence clusters of the phase chimera to incoherence clusters of the amplitude chimera occurs. Moreover, it is established that the noise impact may result in the appearance of a cluster with incoherent behavior in the middle of a coherence cluster.
Anishchenko V. S., Astakhov S. V., Vadivasova T. E.
Diagnostics of the degree of noise influence on a nonlinear system using relative metric entropy
2010, vol. 15, no. 2-3, pp. 261-273
In this paper we summarize and substantiate the relative metric entropy approach introduced in our previous papers [1,2]. Using this approach we study the mixing influence of noise on both regular and chaotic systems. We show that the synchronization phenomenon as well as stochastic resonance decrease, the degree of mixing is caused by white Gaussian noise.