Breaking Synchrony by Heterogeneity in Complex Networks

Details Breaking Synchrony by Heterogeneity in Complex Networks Breaking Synchrony by Heterogeneity in Complex Networks

2003-09-04

arxiv.org/abs/cond-mat/0309103v1

Phys. Rev. Lett. 92, 074103 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.92.074103

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.

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