# Relay synchronization in multiplex networks of discrete maps

## TL;DR

This paper investigates relay synchronization phenomena in three-layer multiplex networks of discrete logistic maps, revealing conditions for complex pattern synchronization and transitions between chimera states.

## Contribution

It introduces a novel analysis of relay synchronization in multiplex networks of discrete maps, including analytical determination of critical coupling strengths.

## Key findings

- Relay synchronization occurs in complex patterns like chimera states.
- Transition from phase to amplitude chimeras with increasing coupling.
- Analytical estimates of critical coupling strengths for phase chimeras.

## Abstract

Complex multiplex networks consist of several subnetwork layers, which interact via pairwise inter-layer connections. Relay synchronization between distant layers which are not directly connected, but only via a relay layer, can be observed in multiplex networks. We study three-layer networks of discrete logistic maps, where each individual layer is a nonlocally coupled ring, and demonstrate scenarios of relay synchronization of complex patterns in the outer layers which interact via an intermediate layer. We find regimes of relay synchronization for chimera states, i.e., patterns of coexisting coherent and incoherent domains, and a transition from phase chimeras to amplitude chimeras for increasing inter-layer coupling. We determine analytically the approximate critical coupling strengths for the existence of phase chimeras.