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28 March 2024
 
  » arxiv » cond-mat/0606073

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Critical behavior and synchronization of discrete stochastic phase coupled oscillators
Kevin Wood ; C. Van den Broeck ; R. Kawai ; Katja Lindenberg ; PostScript ; PDF ; Other formats ;
Date 2 Jun 2006
Subject Statistical Mechanics; Soft Condensed Matter
AbstractSynchronization of stochastic phase-coupled oscillators is known to occur but difficult to characterize because sufficiently complete analytic work is not yet within our reach, and thorough numerical description usually defies all resources. We present a discrete model that is sufficiently simple to be characterized in meaningful detail. In the mean field limit, the model exhibits a supercritical 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, we explicitly rule out multistability and show that that the onset of global synchrony is marked by signatures of the XY universality class. Our numerical results cover dimensions d=2, 3, 4, and 5 and lead to the appropriate XY classical exponents eta and u, a lower critical dimension d_{lc} = 2, and an upper critical dimension d_{uc}=4.
Source arXiv, cond-mat/0606073
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