Desynchronization waves and localized instabilities in oscillator arrays

TL;DR

This paper investigates how heterogeneity in connection strengths causes localized instabilities and desynchronization waves in oscillator arrays, revealing Anderson localization and spreading phenomena.

Contribution

It introduces the use of the master stability function to analyze desynchronization patterns and demonstrates Anderson localization of instability modes in heterogeneous oscillator networks.

Findings

Localized instability modes due to heterogeneity

Desynchronization waves spread across the array

Anderson localization of instability modes

Abstract

We consider a ring of identical or near identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the desynchronization transition that occurs as the coupling strengths are increased. We demonstrate Anderson localization of the modes of instability, and show that such localized instability generates waves of desynchronization that spread to the whole array. Similar results should apply to other networks with regular topology and heterogeneous connection strengths.