Daido Hiroaki, Nakanishi Kenji
Department of Mathematical Sciences, Graduate School of Engineering, Osaka Prefecture University, Sakai 599-8531, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 May;75(5 Pt 2):056206. doi: 10.1103/PhysRevE.75.056206. Epub 2007 May 10.
A population of coupled nonlinear oscillators may age in such a way that the fraction of non-self-oscillatory elements increases. Following our previous paper [Phys. Rev. Lett. 93, 104101 (2004)], we study the effect of aging in this sense mainly for globally coupled Stuart-Landau oscillators with the emphasis on the structure of the (K,p) phase diagram, where K is the coupling strength and p is the ratio of inactive oscillators. In addition to the aging transition reported previously, such a diagram is shown to be characterized by a hornlike region, which we call a "desynchronization horn," where active oscillators desynchronize to form a number of clusters, provided that uncoupled active oscillators are sufficiently nonisochronous. We also show that desynchronization in such a region can be captured as a type of diffusion-induced inhomogeneity based on a "swing-by mechanism." Our results suggest that the desynchronization horn with some curious properties may be a fairly common feature in aging systems of globally and diffusively coupled periodic oscillators.
一群耦合的非线性振荡器可能会以非自振荡元件的比例增加的方式老化。遵循我们之前的论文[《物理评论快报》93, 104101 (2004)]，我们主要研究这种意义上的老化对全局耦合的斯图尔特 - 朗道振荡器的影响，重点关注(K, p)相图的结构，其中K是耦合强度，p是不活跃振荡器的比例。除了先前报道的老化转变外，这样的相图还显示出一个角状区域的特征，我们称之为“去同步角”，在这个区域中，活跃振荡器去同步形成许多簇，前提是未耦合的活跃振荡器足够非等时。我们还表明，基于“掠过机制”，这种区域中的去同步可以被捕获为一种扩散诱导的不均匀性。我们的结果表明，具有一些奇特性质的去同步角可能是全局和扩散耦合的周期振荡器老化系统中相当常见的特征。
