Synchronization scenarios in three-layer networks with a hub

TL;DR

This paper investigates how a single hub node influences synchronization and chimera states in a three-layer neuronal network with non-local coupling, revealing parameter regions where complex synchronized patterns emerge or are suppressed.

Contribution

It introduces a model of three-layer networks with a hub node and analyzes how the hub affects chimera states and synchronization, including effects of coupling strength, delay, and link dilution.

Findings

Double chimeras occur in specific parameter regions.

The hub can induce chimera states even when they don't exist in isolated layers.

Link dilution impacts the stability and nature of synchronized states.

Abstract

We study various relay synchronization scenarios in a three-layer network, where the middle (relay) layer is a single node, i.e. a hub, The two remote layers consist of non-locally coupled rings of FitzHugh-Nagumo oscillators modelling neuronal dynamics. All nodes of the remote layers are connected to the hub. The role of the hub and its importance for the existence of chimera states is investigated in dependence on the inter-layer coupling strength and inter-layer time delay. Tongue-like regions in the parameter plane exhibiting double chimeras, i.e., chimera states in the remote layers whose coherent cores are synchronized with each other, and salt-and-pepper states are found. At very low intra-layer coupling strength, when chimera states do not exist in single layers, these may be induced by the hub. Also the influence of dilution of links between the remote layers and the hub upon the dynamics is investigated. The greatest effect of dilution is observed when links to the coherent domain of the chimeras are removed.