Random heterogeneity outperforms design in network synchronization

Abstract

A widely held assumption on network dynamics is that similar components are more likely to exhibit similar behavior than dissimilar ones and that generic differences among them are necessarily detrimental to synchronization. Here, we show that this assumption does not generally hold in oscillator networks when communication delays are present. We demonstrate, in particular, that random parameter heterogeneity among oscillators can consistently rescue the system from losing synchrony. This finding is supported by electrochemical-oscillator experiments performed on a multielectrode array network. Remarkably, at intermediate levels of heterogeneity, random mismatches are more effective in promoting synchronization than parameter assignments specifically designed to facilitate identical synchronization. Our results suggest that, rather than being eliminated or ignored, intrinsic disorder in technological and biological systems can be harnessed to help maintain coherence required for function.