Delay controls chimera relay synchronization in multiplex networks

TL;DR

This paper investigates how time delays in multilayer networks can control chimera states and remote synchronization, revealing that relay layers influence synchronization patterns in complex systems.

Contribution

It introduces delay as a control mechanism for chimera and relay synchronization in multilayer networks, highlighting the role of relay layer topology.

Findings

Delay controls partial synchronization patterns.

Relay layer topology affects synchronization.

Chimera states can be remotely synchronized across layers.

Abstract

We study remote (or relay) synchronization in multilayer networks between parts of one layer and their counterparts in a second layer, where these two layers are not directly connected. A simple realization of such a system is a triplex network where a relay layer in the middle, which is generally not synchronized, acts as a transmitter between two outer layers. We establish time delay in the inter-layer coupling as a powerful tool to control various partial synchronization patterns, in particular chimera states, i.e., complex patterns of coexisting coherent and incoherent domains. We demonstrate that the three-layer structure of the network allows for synchronization of the coherent domains of chimera states in the first layer with their counterparts in the third layer, whereas the incoherent domains either remain desynchronized or synchronized. By varying the topology of the relay layer, we study its influence on the remote synchronization in the outer layers. As model dynamics we use the paradigmatic FitzHugh-Nagumo system.