网络的网络中的同步：异质振子相互作用群体系统中相干集体行为的开始
Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
摘要：
研究了网络的网络中同步的发生。具体来说，我们考虑网络的相互作用的相位振荡器中的一组振荡器是由几个不同的人口。给定总体中的振子是异质的，因为它们的自然频率来自给定的分布，并且每个总体都有自己的这种分布。振子之间的耦合是全球性的，然而，我们允许不同人口的成员之间的耦合强度分别指定。我们确定的临界条件的相干集体行为的发病，并制定说明性的情况下，振荡器的频率是从一组（可能不同）柯西-洛伦兹分布。一个动机来自神经生物学，其中几个相互作用的振荡器群体（如兴奋性和抑制性神经元和神经胶质）的集体动力学是有趣的。
英文摘要：
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a given population are heterogeneous in that their natural frequencies are drawn from a given distribution, and each population has its own such distribution. The coupling among the oscillators is global, however, we permit the coupling strengths between the members of different populations to be separately specified. We determine the critical condition for the onset of coherent collective behavior, and develop the illustrative case in which the oscillator frequencies are drawn from a set of (possibly different) Cauchy-Lorentz distributions. One motivation is drawn from neurobiology, in which the collective dynamics of several interacting populations of oscillators (such as excitatory and inhibitory neurons and glia) are of interest.
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