有向小世界网络中同相振子的同步跃迁
Synchronization Transition of Identical Phase Oscillators in a Directed Small-World Network
摘要：
我们数值研究了吸引耦合，同相振荡器组成的有向小世界网络。虽然完全同步总是稳定的，但它并不总是从随机初始条件可达的。依赖于捷径密度和相位耦合函数的不对称性，存在持续混沌动力学的制度。通过增加捷径的密度或降低相位耦合函数的不对称性，我们观察到系统同步能力的不连续转变。使用控制技术，我们确定的序参量的分岔情况。我们还讨论了动力学和拓扑学之间的关系，并评论同步过渡的相似性定向渗流。
英文摘要：
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on the shortcut density and on the asymmetry of the phase coupling function, there exists a regime of persistent chaotic dynamics. By increasing the density of shortcuts or decreasing the asymmetry of the phase coupling function, we observe a discontinuous transition in the ability of the system to synchronize. Using a control technique, we identify the bifurcation scenario of the order parameter. We also discuss the relation between dynamics and topology and remark on the similarity of the synchronization transition to directed percolation.
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