Breaking Synchrony by Heterogeneity in Complex Networks

TL;DR

This paper shows that heterogeneity in complex networks of pulse-coupled oscillators disrupts synchrony, leading to stable periodic firing patterns, and provides methods to predict and design these patterns based on network heterogeneity.

Contribution

It introduces a theoretical framework for understanding how coupling heterogeneity affects synchrony and pattern formation in complex oscillator networks, including design principles for specific patterns.

Findings

Heterogeneity replaces global synchrony with stable periodic patterns.

Critical disorder level leads to transition from patterned to asynchronous states.

Self-consistency equations enable prediction of pattern structure from heterogeneity.

Abstract

For networks of pulse-coupled oscillators with complex connectivity, we demonstrate that in the presence of coupling heterogeneity precisely timed periodic firing patterns replace the state of global synchrony that exists in homogenous networks only. With increasing disorder, these patterns persist until they reach a critical temporal extent that is of the order of the interaction delay. For stronger disorder these patterns cease to exist and only asynchronous, aperiodic states are observed. We derive self-consistency equations to predict the precise temporal structure of a pattern from the network heterogeneity. Moreover, we show how to design heterogenous coupling architectures to create an arbitrary prescribed pattern.