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.
Highlights
During the early eighteenth century, Leonhard Euler published a paper on The Seven Bridges of Königsberg providing a mathematical background on vertices and edges [1]
Time delays represent an essential factor in real-world networks due to the finite speed of information propagating through channels connecting the nodes
In the present work we demonstrate that just the variation of delay values in the intra- and inter-layer edges can lead to various dynamical states and allows for control of spatiotemporal patterns
Summary
During the early eighteenth century, Leonhard Euler published a paper on The Seven Bridges of Königsberg providing a mathematical background on vertices and edges [1]. We study the role of the interplay of intra- and inter-layer time delays for the emergence of chimera states in a multi(tri)plex network. Time delays represent an essential factor in real-world networks due to the finite speed of information propagating through channels connecting the nodes. They play a crucial role in determining the dynamical behavior of a complex system [26,27,28,29,30,31,32]. In the present work we demonstrate that just the variation of delay values in the intra- and inter-layer edges can lead to various dynamical states and allows for control of spatiotemporal patterns.
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