Exact and Approximate Stability Conditions for Cluster Synchronization of Kuramoto Oscillators
Exact and Approximate Stability Conditions for Cluster Synchronization of Kuramoto Oscillators
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DOI：
10.23919/acc.2019.8814837
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发表时间：
2019-07
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影响因子：
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通讯作者：
Tommaso Menara;Giacomo Baggio;D. Bassett;F. Pasqualetti
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文献类型：
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作者：
Tommaso Menara;Giacomo Baggio;D. Bassett;F. Pasqualetti
在本文中，我们推导出精确和近似条件的（本地）稳定性的集群同步流形稀疏互连振荡器的异质和加权仓本动力学。当振荡器可以以它们的相位在每个组内随时间保持相同的方式被划分时，集群同步就出现了，这对于从电网到人脑的技术和生物系统中的正常和异常行为至关重要。然而，尽管它的重要性，集群同步得到了有限的关注，使重要类的振荡网络的基本机制调节集群同步仍然是未知的。本文给出了具有仓本动力学的一般加权非均匀振子网络的簇同步流形稳定性的第一条件。特别是，我们讨论了如何现有的结果是不适用的或不足以表征集群同步的稳定性与仓本动力学振荡器，提供严格的定量条件，揭示了网络的权重和振荡器的自然频率调节集群同步，并提供例子来量化我们的条件的紧密性。此外，我们开发的近似条件，尽管其启发式的性质，数值上显示，紧紧抓住集群同步流形的稳定过渡。
In this paper we derive exact and approximate conditions for the (local) stability of the cluster synchronization manifold for sparsely interconnected oscillators with heterogeneous and weighted Kuramoto dynamics. Cluster synchronization, which emerges when the oscillators can be partitioned in a way that their phases remain identical over time within each group, is critically important for normal and abnormal behaviors in technological and biological systems ranging from the power grid to the human brain. Yet, despite its importance, cluster synchronization has received limited attention, so that the fundamental mechanisms regulating cluster synchronization in important classes of oscillatory networks are still unknown. In this paper we provide the first conditions for the stability of the cluster synchronization manifold for general weighted networks of heterogeneous oscillators with Kuramoto dynamics. In particular, we discuss how existing results are inapplicable or insufficient to characterize the stability of cluster synchronization for oscillators with Kuramoto dynamics, provide rigorous quantitative conditions that reveal how the network weights and oscillators' natural frequencies regulate cluster synchronization, and offer examples to quantify the tightness of our conditions. Further, we develop approximate conditions that, despite their heuristic nature, are numerically shown to tightly capture the transition to stability of the cluster synchronization manifold.