Abstract
We explore the bifurcation transition from coherence to incoherence in an ensemble of nonlocally coupled logistic maps. It is shown that two types of chimera states, namely amplitude and phase, can be found in this network. We reveal a bifurcation mechanism by analyzing the evolution of space-time profiles and the coupling function with varying coupling coefficient and formulate the conditions for realizing the chimera states in the ensemble. The regularities are established for the evolution of cross-correlations of oscillations in the network elements at the bifurcations related to the coupling strength variation. We reveal the features of cross-correlations for phase and amplitude chimera states. It is also shown that the effect of time intermittency between the amplitude and phase chimeras can be realized in the considered ensemble.
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Acknowledgements
The authors acknowledge support from SFB910. Vadim S. Anishchenko, acknowledges support from the Russian Science Foundation (grant No. 16-12-10175). Tatiana E. Vadivasova and Galina I. Strelkova acknowledge support from RFBR (grants No. 14-52-12002 and No. 15-02-02288).
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Anishchenko, V.S., Vadivasova, T.E., Strelkova, G.I. (2017). Coherence–Incoherence Transition and Properties of Different Types of Chimeras in a Network of Nonlocally Coupled Chaotic Maps. In: Aranson, I., Pikovsky, A., Rulkov, N., Tsimring, L. (eds) Advances in Dynamics, Patterns, Cognition. Nonlinear Systems and Complexity, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-53673-6_6
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