Synchronization of Discrete Oscillators on Ring Lattices and Small-World Networks

Kevin Liu Rodrigues; Ronald Dickman

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arXiv · 1912.04104

Synchronization of Discrete Oscillators on Ring Lattices and Small-World Networks

Kevin Liu Rodrigues·Ronald Dickman

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Abstract

A lattice of three-state stochastic phase-coupled oscillators introduced by Wood it et al. exhibits a phase transition at a critical value of the coupling parameter $a$, leading to stable global oscillations (GO). On a complete graph, upon further increase in $a$, the model exhibits an infinite-period (IP) phase transition, at which collective oscillations cease and discrete rotational ($C_3$) symmetry is broken. In the case of large negative values of the coupling, Escaff et al. discovered the stability of travelling-wave states with no global synchronization but with local order. Here, we verify the IP phase in systems with long-range coupling but of lower connectivity than a complete graph and show that even for large positive coupling, the system sometimes fails to reach global order. The ensuing travelling-wave state appears to be a metastable configuration whose birth and decay (into the previously described phases) are associated with the initial conditions and fluctuations.

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Kevin Liu Rodrigues, Ronald Dickman. 2019-12-09. Synchronization of Discrete Oscillators on Ring Lattices and Small-World Networks. https://arxiv.org/abs/1912.04104

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