Effects of Disorder on Synchronization of Discrete Phase-Coupled Oscillators

Details Effects of Disorder on Synchronization of Discrete Phase-Coupled Oscillators Effects of Disorder on Synchronization of Discrete Phase-Coupled Oscillators

2006-11-29

arxiv.org/abs/cond-mat/0611757v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of globally connected arrays of N types of oscillators (N=2, 3, 4) by exploring the linear stability of the nonsynchronous fixed point. We also provide results for globally coupled arrays where the transition rate of each unit is drawn from a uniform distribution of finite width. Even in the presence of transition rate disorder, numerical and analytical results point to a single phase transition to macroscopic synchrony at a critical value of the coupling strength. Numerical simulations make possible the further characterization of the synchronized arrays.

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