Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators
Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators
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DOI：
10.1109/tcns.2019.2903914
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发表时间：
2020-03-01
影响因子：
4.2
通讯作者：
Pasqualetti, Fabio
中科院分区：
文献类型：
--
作者：
Menara, Tommaso;Baggio, Giacomo;Pasqualetti, Fabio
在本文中，我们研究了具有异质 Kuramoto 动力学的振荡器网络中的簇同步，其中多组具有相同相位的振荡器共存于一个连接的网络中。集群同步是多种生物和技术过程的基础；然而，实现仓本振荡器簇同步的基本机制仍然难以捉摸。在本文中，我们推导了网络权重、簇配置和振荡器固有频率的定量条件，以确保簇同步流形的渐近稳定性；也就是说，在振荡器状态发生扰动后恢复所需集群同步配置的能力。定性地，我们的结果表明，当簇内耦合比簇间耦合足够强，不同簇中振荡器的固有频率足够不同，或者在两个簇的情况下，当簇内动态均匀时，簇同步是稳定的。我们通过数值研究验证了理论结果的有效性。
In this paper, we study cluster synchronization in networks of oscillators with heterogenous Kuramoto dynamics, where multiple groups of oscillators with identical phases coexist in a connected network. Cluster synchronization is at the basis of several biological and technological processes; yet, the underlying mechanisms to enable the cluster synchronization of Kuramoto oscillators have remained elusive. In this paper, we derive quantitative conditions on the network weights, cluster configuration, and oscillators' natural frequency that ensure the asymptotic stability of the cluster synchronization manifold; that is, the ability to recover the desired cluster synchronization configuration following a perturbation of the oscillators' states. Qualitatively, our results show that cluster synchronization is stable when the intracluster coupling is sufficiently stronger than the intercluster coupling, the natural frequencies of the oscillators in distinct clusters are sufficiently different, or, in the case of two clusters, when the intracluster dynamics is homogeneous. We validate the effectiveness of our theoretical results via numerical studies.