Desynchronization induced by time-varying network

TL;DR

This paper investigates how time-varying network structures can induce desynchronization in arrays of excitable oscillators, revealing a self-consistent instability mechanism and conditions for averaging effects.

Contribution

It introduces an extended averaging theorem to analyze the impact of network modulation on synchronization and reports oscillation death as a consequence of the instability.

Findings

Time-varying networks can destabilize synchronization.

An extended averaging theorem is developed for partial averages.

Oscillation death occurs following network-driven instability.

Abstract

The synchronous dynamics of an array of excitable oscillators, coupled via a generic graph, is studied. Non homogeneous perturbations can grow and destroy synchrony, via a self-consistent instability which is solely instigated by the intrinsic network dynamics. By acting on the characteristic time-scale of the network modulation, one can make the examined system to behave as its (partially) averaged analog. This result if formally obtained by proving an extended version of the averaging theorem, which allows for partial averages to be carried out. As a byproduct of the analysis, oscillation death are reported to follow the onset of the network driven instability.