Barreto Ernest, Hunt Brian, Ott Edward, So Paul
Department of Physics & Astronomy, The Center for Neural Dynamics and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, VA 22030, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Mar;77(3 Pt 2):036107. doi: 10.1103/PhysRevE.77.036107. Epub 2008 Mar 6.
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.
研究了网络的网络中的同步起始。具体而言，我们考虑相互作用的相位振荡器网络，其中振荡器组由几个不同的群体组成。给定群体中的振荡器是异质的，因为它们的固有频率是从给定分布中抽取的，并且每个群体都有其自己的这样的分布。振荡器之间的耦合是全局的，然而，我们允许不同群体的成员之间的耦合强度分别指定。我们确定了相干集体行为起始的临界条件，并发展了振荡器频率从一组（可能不同的）柯西 - 洛伦兹分布中抽取的示例情况。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以及神经胶质细胞）的集体动力学是令人感兴趣的。
