Erosion of synchronization: Coupling heterogeneity and network structure

TL;DR

This paper analyzes how heterogeneity in network structure and coupling functions causes the loss of perfect synchronization in coupled oscillators, providing analytical predictions and validating them through simulations.

Contribution

It extends previous work by deriving analytical formulas for synchronization erosion considering heterogeneous coupling functions and network structures.

Findings

Heterogeneous coupling leads to complete erosion of synchronization.

Analytical predictions match numerical simulations across various network models.

Certain network structures with known spectral properties allow further analytical insights.

Abstract

We study the dynamics of network-coupled phase oscillators in the presence of coupling frustration. It was recently demonstrated that in heterogeneous network topologies, the presence of coupling frustration causes perfect phase synchronization to become unattainable even in the limit of infinite coupling strength. Here, we consider the important case of heterogeneous coupling functions and extend previous results by deriving analytical predictions for the total erosion of synchronization. Our analytical results are given in terms of basic quantities related to the network structure and coupling frustration. In addition to fully heterogeneous coupling, where each individual interaction is allowed to be distinct, we also consider partially heterogeneous coupling and homogeneous coupling in which the coupling functions are either unique to each oscillator or identical for all network interactions, respectively. We demonstrate the validity of our theory with numerical simulations of multiple network models, and highlight the interesting effects that various coupling choices and network models have on the total erosion of synchronization. Finally, we consider some special network structures with well-known spectral properties, which allows us to derive further analytical results.