We show that disorder in the form of random oscillator heterogeneity can consistently rescue networks from losing synchronized rhythm. 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.
Disorder can be better than design. 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. Recently, we showed that this assumption does not generally hold in oscillator networks when communication delays are present. We demonstrated, 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 multi-electrode 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.
Synchronizing chaos with disorder. The results above can be further extended to chaotic systems, which we demonstrated experimentally using networks of Chua’s oscillators. Moreover, we proposed a general mechanism based on heterogeneity-induced mode mixing that provides insights into the observed phenomenon. Since individual differences are ubiquitous and often unavoidable in real systems, it follows that such imperfections can be an unexpected source of synchronization stability.
Below is a short animation demonstrating the key finding of our study. It shows the dynamics of four oscillator networks that are identical to each other except the amount of disorder in the system. The system with no disorder and the one with strong disorder both lose synchrony and become incoherent; systems with intermediate disorder, however, are able to maintain a synchronized rhythm indefinitely.
- Y. Zhang, J. L. Ocampo-Espindola, I. Z. Kiss, and A. E. Motter, Random heterogeneity outperforms design in network synchronization, Proc. Natl. Acad. Sci. U.S.A. 118, e2024299118 (2021)
- Y. Sugitani*, Y. Zhang*, and A. E. Motter, Synchronizing chaos with imperfections, Phys. Rev. Lett. 126, 164101 (2021)