Synchronization-Desynchronization Transitions in Complex Networks: An Interplay of Distributed Time Delay and Inhibitory Nodes

TL;DR

This paper explores how distributed time delays and the balance of inhibitory and excitatory nodes influence synchronization stability in complex oscillator networks, revealing conditions for resynchronization transitions.

Contribution

It introduces an analytical network model to study the effects of distributed delays and inhibitory ratios on synchronization in coupled Stuart--Landau oscillators.

Findings

Synchronization becomes unstable beyond a critical inhibition ratio.

Increasing delay distribution width can restore synchronization.

Resynchronization transitions occur at high inhibition ratios.

Abstract

We investigate the combined effects of distributed delay and the balance between excitatory and inhibitory nodes on the stability of synchronous oscillations in a network of coupled Stuart--Landau oscillators. To this end a network model is proposed for which the stability can be investigated analytically. It is found that beyond a critical inhibition ratio synchronization tends to be unstable. However, increasing distributional widths can counteract this trend leading to multiple resynchronization transitions at relatively high inhibition ratios. All studies are performed on two distribution types, a uniform distribution and a Gamma distribution.