Solitary states in adaptive nonlocal oscillator networks
Solitary states in adaptive nonlocal oscillator networks
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DOI：
10.1140/epjst/e2020-900253-0
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发表时间：
2020-09-01
影响因子：
2.8
通讯作者：
Yanchuk, Serhiy
中科院分区：
文献类型：
--
作者：
Berner, Rico;Polanska, Alicja;Yanchuk, Serhiy
在这篇文章中，我们分析了自适应耦合相位振荡器的非局部环形网络。我们观察到各种频率同步的状态，如锁相，多集群和孤立的状态。对于一个重要的子类的锁相解决方案，旋转波，我们提供了严格的稳定性分析。分析表明，它们的稳定性对耦合结构和波数有很强的依赖性，这与全对全耦合网络有很大的不同。尽管在大量的动力学系统中已经观察到了孤立态，但在文献中基本上没有讨论它们出现背后的机制。在这里，我们将展示如何孤立的状态出现由于网络的自适应功能，并分类几个分叉的情况下，这些国家的创建和稳定。
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the phase-locked solutions, the rotating waves, we provide a rigorous stability analysis. This analysis shows a strong dependence of their stability on the coupling structure and the wavenumber which is a remarkable difference to an all-to-all coupled network. Despite the fact that solitary states have been observed in a plethora of dynamical systems, the mechanisms behind their emergence were largely unaddressed in the literature. Here, we show how solitary states emerge due to the adaptive feature of the network and classify several bifurcation scenarios in which these states are created and stabilized.