Critical behavior and synchronization of discrete stochastic phase-coupled oscillators
Abstract
Synchronization 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 that we characterize numerically using finite-size scaling analysis. In particular, we explicitly rule out multistability and show 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 β and ν , a lower critical dimension dlc=2 , and an upper critical dimension duc=4 .
- Publication:
-
Physical Review E
- Pub Date:
- September 2006
- DOI:
- 10.1103/PhysRevE.74.031113
- arXiv:
- arXiv:cond-mat/0606073
- Bibcode:
- 2006PhRvE..74c1113W
- Keywords:
-
- 64.60.Ht;
- 05.45.Xt;
- 89.75.-k;
- Dynamic critical phenomena;
- Synchronization;
- coupled oscillators;
- Complex systems;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Soft Condensed Matter