Effects of Disorder on Synchronization of Discrete Phase-Coupled Oscillators

Abstract

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.

References in corpus (3)

• The universality of synchrony: critical behavior in a discrete model of stochastic phase coupled oscillators
• Critical behavior and synchronization of discrete stochastic phase coupled oscillators
• Universal critical behavior of noisy coupled oscillators: A renormalization group study

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• Synchronization and phase redistribution in self-replicating populations of coupled oscillators and excitable elements
• Nonlinear transport effects in mass separation by effusion
• Dissipation enables robust extensive scaling of multipartite correlations
• Macroscopic theory of multipartite correlations in permutation-invariant open quantum systems
• Synchronization of thermodynamically consistent stochastic phase oscillators