嵌合体展开
Chimeras unfolded
摘要：
耦合相位振荡器的仓本模型中的混合不稳定性是理解一系列时空模式的关键，这些模式在从神经网络到耦合激光器到电网的系统的集体动力学中具有突出的特征。在本文中，我们描述了一个余维-2分叉的混合，其展开，除了经典的情况下的发病同步，也解释了集群和嵌合体的形成。我们使用线性稳定性分析和彭罗斯图的组合来识别和分析各种时空模式，包括静止和旅行相干集群和扭曲状态，以及它们与称为嵌合体状态的非相干行为区域的组合。线性稳定性分析用于估计这些结构内的速度分布。另一方面，彭罗斯图解准确地预测了它们存在的盆地。此外，我们表明，网络拓扑结构可以赋予嵌合态与非平凡的空间组织。特别是，我们提出了扭曲的嵌合体状态，其相干区域被组织为固定或旅行扭曲状态。分析结果示出数值分岔图计算的仓本模型与单，双，和三模态频率分布和所有到所有和非本地最近邻连接。
英文摘要：
The instability of mixing in the Kuramoto model of coupled phase oscillators is the key to understanding a range of spatiotemporal patterns, which feature prominently in collective dynamics of systems ranging from neuronal networks, to coupled lasers, to power grids. In this paper, we describe a codimension-2 bifurcation of mixing whose unfolding, in addition to the classical scenario of the onset of synchronization, also explains the formation of clusters and chimeras. We use a combination of linear stability analysis and Penrose diagrams to identify and analyze a variety of spatiotemporal patterns including stationary and traveling coherent clusters and twisted states, as well as their combinations with regions of incoherent behavior called chimera states. The linear stability analysis is used to estimate of the velocity distribution within these structures. Penrose diagrams, on the other hand, predict accurately the basins of their existence. Furthermore, we show that network topology can endow chimera states with nontrivial spatial organization. In particular, we present twisted chimera states, whose coherent regions are organized as stationary or traveling twisted states. The analytical results are illustrated with numerical bifurcation diagrams computed for the Kuramoto model with uni-, bi-, and tri-modal frequency distributions and all-to-all and nonlocal nearest-neighbor connectivity.
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