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.

中文翻译：

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环格和小世界网络上离散振荡器的同步

Wood it 等人介绍的三态随机相位耦合振荡器的晶格。在耦合参数 $a$ 的临界值处表现出相变，导致稳定的全局振荡 (GO)。在完整的图形上，随着 $a$ 的进一步增加，模型呈现出无限周期 (IP) 相变，此时集体振荡停止并且离散旋转 ($C_3$) 对称性被破坏。在耦合负值较大的情况下，Essaff 等人。发现了没有全局同步但具有局部顺序的行波状态的稳定性。在这里，我们验证了具有远距离耦合但连接性低于完整图的系统中的 IP 阶段，并表明即使对于大的正耦合，系统有时也无法达到全局顺序。