Synchronizing noisy nonidentical oscillators by transient uncoupling

TL;DR

This paper demonstrates that transient uncoupling can induce and stabilize generalized synchronization among nonidentical chaotic oscillators, even under noise, by selectively uncoupling in diverging phase space regions.

Contribution

It extends the concept of transient uncoupling to nonidentical units and introduces a method to select uncoupling regions based on local divergence measures.

Findings

Transient uncoupling achieves generalized synchronization in nonidentical chaotic units.

It stabilizes synchronization against common noise.

Uncoupling in diverging phase space regions enhances synchronization stability.

Abstract

Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them -- a phenomenon termed "generalized synchronization." Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.