时滞耦合振子网络中幅值死亡的主稳定岛
Master Stability Islands for Amplitude Death in Networks of Delay-Coupled Oscillators
摘要：
本文提出了一种分析延迟耦合振荡器网络幅死稳定性的主稳定函数方法。与熟悉的MSF瞬时耦合网络，通常有一个单一的输入编码的网络拉普拉斯矩阵的特征值的影响，延迟耦合网络，我们表明，这样的MSF一般需要两个额外的输入：时间延迟和耦合强度。为了利用MSF预测任意网络的AD的稳定性，对于一个选定的非线性系统（节点动态）和耦合函数，我们引入了主稳定性岛（MSI）的概念，这是二维的稳定性岛的延迟耦合空间与第三维（“海拔”）编码的特征值，导致稳定的AD。我们计算的MSFs和相应的MSIs几个常见的混沌系统，包括Rossler，Lorenz，和陈的系统，并发现，它通常是可能的，以实现AD和非零的时间延迟是必要的AD状态的稳定。
英文摘要：
This paper presents a master stability function (MSF) approach for analyzing the stability of amplitude death (AD) in networks of delay-coupled oscillators. Unlike the familiar MSFs for instantaneously coupled networks, which typically have a single input encoding for the effects of the eigenvalues of the network Laplacian matrix, for delay-coupled networks we show that such MSFs generally require two additional inputs: the time delay and the coupling strength. To utilize the MSF for predicting the stability of AD of arbitrary networks for a chosen nonlinear system (node dynamics) and coupling function, we introduce the concept of master stability islands (MSIs), which are two-dimensional stability islands of the delay-coupling space together with a third dimension ("altitude") encoding for eigenvalues that result in stable AD. We compute the MSFs and show the corresponding MSIs for several common chaotic systems including the Rossler, the Lorenz, and Chen's system, and found that it is generally possible to achieve AD and that a nonzero time delay is necessary for the stabilization of the AD states.
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