Erosion of synchronization in networks of coupled oscillators

TL;DR

This paper investigates how synchronization in networks of coupled oscillators is fundamentally limited by structural and coupling factors, revealing a phenomenon called erosion where perfect synchronization cannot be achieved.

Contribution

It introduces the concept of erosion of synchronization, analyzing its dependence on coupling frustration and network heterogeneity, and shows how oscillator organization shifts to node degree-based patterns.

Findings

Erosion of synchronization is separable into coupling frustration and structural heterogeneity effects.

Erosion increases with both coupling frustration and network heterogeneity.

Oscillators reorganize according to node degree rather than natural frequency during erosion.

Abstract

We report erosion of synchronization in networks of coupled phase oscillators, a phenomenon where perfect phase synchronization is unattainable in steady-state, even in the limit of infinite coupling. An analysis reveals that the total erosion is separable into the product of terms characterizing coupling frustration and structural heterogeneity, both of which amplify erosion. The latter, however, can differ significantly from degree heterogeneity. Finally, we show that erosion is marked by the reorganization of oscillators according to their node degrees rather than their natural frequencies.