Loss of synchronization in complex neuronal networks with delay

TL;DR

This paper studies how delay and inhibitory links affect synchronization stability in neural networks, revealing that excitatory networks are stable regardless of delay, but small-world networks can desynchronize with enough inhibition.

Contribution

It introduces a master stability function approach to analyze delay-coupled neural networks and uncovers how inhibitory links induce desynchronization in small-world topologies.

Findings

Synchronization is stable for excitatory networks regardless of delay.

Inhibitory links cause a phase transition to desynchronization.

Small-world networks are more susceptible to inhibition-induced desynchronization.

Abstract

We investigate the stability of synchronization in networks of delay-coupled excitable neural oscillators. On the basis of the master stability function formalism, we demonstrate that synchronization is always stable for excitatory coupling independently of the delay and coupling strength. Superimposing inhibitory links randomly on top of a regular ring of excitatory coupling, which yields a small-world-like network topology, we find a phase transition to desynchronization as the probability of inhibitory links exceeds a critical value. We explore the scaling of the critical value in dependence on network properties. Compared to random networks, we find that small-world topologies are more susceptible to desynchronization via inhibition.