Synchronization of networks of oscillators with distributed delay coupling

TL;DR

This paper investigates the stability of synchronized states in oscillator networks with distributed delay coupling, introducing a generalized master stability function approach and analyzing various delay distributions and network topologies.

Contribution

It develops a semi-analytic method to determine stability of synchronization in networks with distributed delays using Floquet exponents.

Findings

Stability of synchronized states can be assessed semi-analytically.

Different delay distributions and network topologies affect synchronization stability.

The approach applies to various practical network configurations.

Abstract

This paper studies the stability of synchronized states in networks where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of Stuart-Landau oscillators, it is shown how the stability of synchronized solutions in networks with distributed delay coupling can be determined through a semi-analytic computation of Floquet exponents. The analysis of stability of fully synchronized and of cluster or splay states is illustrated for several practically important choices of delay distributions and network topologies.