Chimeras in Multiplex Networks: Interplay of Inter- and Intra-Layer Delays

Abstract

Complex networks consisting of several interacting layers allow for special dynamics caused by time delay. We study the scenarios of time delay induced patterns in a three-layer network of FitzHugh-Nagumo oscillators, where each layer has a nonlocal coupling topology. Varying the time delay in the connections, we observe chimera states, i.e., complex spatio-temporal patterns of coexisting coherent and incoherent domains. In particular, we focus on the interplay of time delay in the intra-layer and inter-layer coupling term. In the parameter plane of the two delay times we find regions of existence of chimera states alternating with coherent dynamics. Moreover, in the presence of time delay we detect full and relay inter-layer synchronization.