Collective behavior of coupled nonuniform stochastic oscillators

Details Collective behavior of coupled nonuniform stochastic oscillators Collective behavior of coupled nonuniform stochastic oscillators

2012-01-27

arxiv.org/abs/1201.5854v1

Physica A 391 (2012) 1900--1906

Physics

Data Analysis, Statistics and Probability

17 pages, 4 figures

Scientific paper

10.1016/j.physa.2011.10.012

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.

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