State-dependent effective interactions in oscillator networks through coupling functions with dead zones
State-dependent effective interactions in oscillator networks through coupling functions with dead zones
复制标题
通过与死区的耦合函数在振荡器网络中进行状态相关的有效交互
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Camille Poignard
中科院分区：
文献类型：
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作者：
P. Ashwin;C. Bick;Camille Poignard
相互作用的动力系统网络的动力学取决于各个单元之间耦合的性质。我们研究了具有耦合函数的振荡单元网络，这些网络具有“死区”，即耦合函数在具有内部的集合上为零。对于这样的网络，观察单元之间的有效相互作用而不是(固定的)结构连通性来理解网络动态是方便的。例如，振荡器可以在特定的相位配置中有效地去耦合。沿着轨道，有效的相互作用不一定是静态的，但有效的耦合可能会随着时间的推移而演变。在这里，我们形式化死区和有效交互的概念。我们阐明了耦合函数如何塑造可能的有效相互作用方案，以及它们如何随时间演变。本文是“耦合作用：物理、生物和社会科学中的动力相互作用机制”主题的一部分。
The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling functions that have ‘dead zones’, that is the coupling functions are zero on sets with interior. For such networks, it is convenient to look at the effective interactions between units rather than the (fixed) structural connectivity to understand the network dynamics. For example, oscillators may effectively decouple in particular phase configurations. Along trajectories, the effective interactions are not necessarily static, but the effective coupling may evolve in time. Here, we formalize the concepts of dead zones and effective interactions. We elucidate how the coupling function shapes the possible effective interaction schemes and how they evolve in time. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.