Chen Yuehua, Xiao Jinghua, Liu Weiqing, Li Lixiang, Yang Yixian
School of Science, Beijing University of Posts and Telecommunications, Beijing, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046206. doi: 10.1103/PhysRevE.80.046206. Epub 2009 Oct 14.
Together with attractive couplings, repulsive couplings play crucial roles in determining important evolutions in natural systems, such as in learning and oscillatory processes of neural networks. The complex interactions between them have great influence on the systems. A detailed understanding of the dynamical properties under this type of couplings is of practical significance. In this paper, we propose a model to investigate the dynamics of attractive and repulsive couplings, which give rise to rich phenomena, especially for amplitude death (AD). The relationship among various dynamics and possible transitions to AD are illustrated. When the system is in the maximally stable AD, we observe the transient behavior of in-phase (high frequency) and out-of-phase (low frequency) motions. The mechanism behind the phenomenon is given.
排斥耦合与吸引耦合一起，在决定自然系统中的重要演化过程中起着关键作用，例如在神经网络的学习和振荡过程中。它们之间的复杂相互作用对系统有很大影响。详细了解这种类型耦合下的动力学特性具有实际意义。在本文中，我们提出了一个模型来研究吸引耦合和排斥耦合的动力学，这会产生丰富的现象，特别是对于振幅死亡（AD）。阐述了各种动力学之间的关系以及向AD的可能转变。当系统处于最大稳定AD状态时，我们观察到同相（高频）和异相（低频）运动的瞬态行为。给出了该现象背后的机制。
