Reentrant transition in coupled noisy oscillators

TL;DR

This paper discovers a reentrant transition in coupled noisy oscillators, where increasing coupling strength leads to a cycle of synchronization and phase slipping, revealing complex dynamics beyond traditional models.

Contribution

It introduces a novel reentrant transition phenomenon in noisy oscillators and provides a theoretical framework using the Fokker-Planck equation, validated by the Brusselator model.

Findings

Reentrant transition between synchronized and phase slip states.

Increased coupling causes more frequent phase slips.

Theoretical predictions match numerical simulations.

Abstract

We report on a novel type of instability observed in a noisy oscillator unidirectionally coupled to a pacemaker. Using a phase oscillator model, we find that, as the coupling strength is increased, the noisy oscillator lags behind the pacemaker more frequently and the phase slip rate increases, which may not be observed in averaged phase models such as the Kuramoto model. Investigation of the corresponding Fokker-Planck equation enables us to obtain the reentrant transition line between the synchronized state and the phase slip state. We verify our theory using the Brusselator model, suggesting that this reentrant transition can be found in a wide range of limit cycle oscillators.