Collective behavior of coupled nonuniform stochastic oscillators

TL;DR

This paper investigates how nonuniform stochastic oscillators behave collectively, revealing phase transitions and the loss of collective oscillations as nonuniformity increases, with a focus on stability and excitable states.

Contribution

It extends existing models by introducing nonuniformity in stochastic oscillators and analyzes the resulting phase transitions and stability conditions.

Findings

Multiple phase transitions predicted by mean field analysis.

Collective oscillations are stable only for certain nonuniformity levels.

At maximum nonuniformity, oscillators become excitable with no collective oscillations.

Abstract

Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the literature, with equal transition rates among the states. Here we start from the model recently introduced by Wood et al. [Phys. Rev. Lett. 96}, 145701 (2006)], which has a collectively synchronized phase, and parametrically modify the phase-coupled oscillators to render them (stochastically) nonuniform. We show that, depending on the nonuniformity parameter $0\leq \alpha \leq 1$, a mean field analysis predicts the occurrence of several phase transitions. In particular, the phase with collective oscillations is stable for the complete graph only for $\alpha \leq \alpha^\prime < 1$. At $\alpha=1$ the oscillators become excitable elements and the system has an absorbing state. In the excitable regime, no collective oscillations were found in the model.