Synchronization scenarios in three-layer networks with a hub

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 modeling 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 are 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 the 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. Published under an exclusive license by AIP Publishing.

Automated summary

This study investigates various relay synchronization scenarios in a three-layer network, focusing on the role of the hub node and its impact on the existence of chimera states, depending on the inter-layer coupling strength and time delay. The findings include regions in the parameter plane exhibiting double chimeras and salt-and-pepper states, as well as the induction of chimera states by the hub in the absence of such states in individual layers. Additionally, the influence of link dilution between the remote layers and the hub on dynamics is examined, with the greatest effect observed when links to the coherent domain of the chimeras are removed.