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The universality of synchrony: critical behavior in a discrete model of stochastic phase coupled oscillators

Kevin Wood·C. Van den Broeck·R. Kawai·Katja Lindenberg
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Abstract

We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition which we characterize numerically using finite-size scaling analysis. In particular, the onset of global synchrony is marked by signatures of the XY universality class, including the appropriate classical exponents $β$ and $ν$, a lower critical dimension $d_{lc} = 2$, and an upper critical dimension $d_{uc}=4$.

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Kevin Wood, C. Van den Broeck, R. Kawai, Katja Lindenberg. 2005-12-08. The universality of synchrony: critical behavior in a discrete model of stochastic phase coupled oscillators. https://doi.org/10.1103/physrevlett.96.145701

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