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Time-delayed feedback control of coherence resonance chimeras

Zakharova, Anna; Semenova, Nadezhda; Anishchenko, Vadim; Schöll, Eckehard

Using the model of a FitzHugh-Nagumo system in the excitable regime, we investigate the influence of time-delayed feedback on noise-induced chimera states in a network with nonlocal coupling, i.e., coherence resonance chimeras. It is shown that time-delayed feedback allows for the control of the range of parameter values where these chimera states occur. Moreover, for the feedback delay close to the intrinsic period of the system, we find a novel regime which we call period-two coherence resonance chimera. Coherence resonance chimeras in nonlocally coupled networks of excitable elements represent partial synchronization patterns composed of spatially separated domains of coherent and incoherent spiking behavior, which are induced by noise. These patterns are different from classical chimera states occurring in deterministic oscillatory systems and combine properties of the counter-intuitive phenomenon of coherence resonance, i.e., a constructive role of noise, and chimera states, i.e., the coexistence of spatially synchronized and desynchronized domains in a network of identical elements. Another distinctive feature of the particular type of chimera we study here is its alternating behavior, i.e., periodic switching of the location of coherent and incoherent domains. Applying time-delayed feedback, we demonstrate how to control coherence resonance chimeras by adjusting delay time and feedback strength. In particular, we show that feedback increases the parameter intervals of existence of chimera states and has a significant impact on their alternating dynamics leading to the appearance of novel patterns, which we call period-two coherence resonance chimera. Since the dynamics of every individual network element in our study is given by the FitzHugh-Nagumo (FHN) system, which is a paradigmatic model for neurons in the excitable regime, we expect wide-range applications of our results to neural networks.
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science, 10.1063/1.5008385, American Institute of Physics (AIP)
  • This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 27, 114320 (2017) and may be found at https://doi.org/10.1063/1.5008385.