Multiclusters in Networks of Adaptively Coupled Phase Oscillators
Multiclusters in Networks of Adaptively Coupled Phase Oscillators
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DOI：
10.1137/18m1210150
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发表时间：
2019-01-01
影响因子：
2.1
通讯作者：
Yanchuk, Serhiy
中科院分区：
文献类型：
--
作者：
Berner, Rico;Schoell, Eckehard;Yanchuk, Serhiy
具有自适应耦合的网络上的动态系统自然地出现在现实世界的系统中，例如电网网络、社交网络和神经网络。我们研究了一个范例系统的自适应耦合相位振荡器的灵感来自神经网络与突触可塑性。这种系统的一个重要行为揭示了网络分裂成具有相同频率的振荡器集群，其中不同集群对应于不同频率。从单簇解出发，我们给出了多簇解的存在性判据，并给出了它们的显式形式。在一个集群内的振荡器的相位可以组织在不同的模式：对映，双对映，和splay类型。有趣的是，多集群被证明存在于不同的集群表现出不同的模式。例如，对映簇可以与八字簇共存。我们还为单集群和多集群解决方案提供稳定条件。这些条件，特别是，揭示了高水平的多稳态。
Dynamical systems on networks with adaptive couplings appear naturally in real-world systems such as power grid networks, social networks, and neuronal networks. We investigate a paradigmatic system of adaptively coupled phase oscillators inspired by neuronal networks with synaptic plasticity. One important behavior of such systems reveals splitting of the network into clusters of oscillators with the same frequencies, where different clusters correspond to different frequencies. Starting from one-cluster solutions we provide existence criteria for multicluster solutions and present their explicit form. The phases of the oscillators within one cluster can be organized in different patterns: antipodal, double antipodal, and splay type. Interestingly, multiclusters are shown to exist where different clusters exhibit different patterns. For instance, an antipodal cluster can coexist with a splay cluster. We also provide stability conditions for one- and multicluster solutions. These conditions, in particular, reveal a high level of multistability.