Nonstationary chimeras in a neuronal network

¹ School of Mathematics and Physics, China University of Geosciences - Wuhan, 430074, China
² Department of Biomedical Engineering, Amirkabir University of Technology - 424 Hafez Ave., Tehran 15875-4413, Iran
³ Physics and Applied Mathematics Unit, Indian Statistical Institute - 203 B. T. Road, Kolkata 700108, India
⁴ Faculty of Natural Sciences and Mathematics, University of Maribor - Koroška cesta 160, SI-2000 Maribor, Slovenia
⁵ Complexity Science Hub - Josefstädterstraße 39, A-1080 Vienna, Austria
⁶ School of Electronic and Information Engineering, Beihang University - Beijing 100191, China

^(a) matjaz.perc@uni-mb.si

Received: 29 June 2018
Accepted: 20 August 2018

Abstract

Chimeras are special states that are composed of coexisting spatial domains of coherent and incoherent dynamics, which typically emerge in identically coupled oscillators. In this paper, we study a network of nonlocally coupled Hindmarsh-Rose neurons that are subject to an alternating current. We show that chimera states emerge when the neurons are connected through electrical synapses. The considered model has two coexisting attractors, namely a limit cycle and a chaotic attractor, to which the dynamics converges in dependence on the initial conditions. While earlier research reported the existence of chimeras in Hindmarsh-Rose neuronal networks mainly through chemical synapses, here we show that an alternating current in an electrically coupled network can also evoke chimeras, whereby the spatial positions of coherent and incoherent domains vary with time. Remarkably, we also observe chimera states in locally coupled neurons through electrical synapses, which reduce the relaxation of nonlocallity in the coupling configuration. The existence of nonstationary chimeras is confirmed by means of a local order parameter.