Synchronisation in networks of delay-coupled type-I excitable systems

TL;DR

This paper investigates how delay and coupling strength affect synchronization stability in networks of type-I excitable systems, revealing complex behaviors including multiple transitions between synchronized and desynchronized states.

Contribution

It applies the Master Stability Function to analyze synchronization in delay-coupled type-I systems, uncovering parameter-dependent stability and complex transition phenomena.

Findings

Synchronization stability depends on coupling parameters in type-I systems.

Adding inhibitory links can both destabilize and restabilize synchronization.

Multiple transitions between synchronization and desynchronization occur in excitable and oscillatory networks.

Abstract

We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones.