Chen Lijia, Ji Peng, Waxman David, Lin Wei, Kurths Juergen
Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China.
Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany.
Chaos. 2019 Aug;29(8):083131. doi: 10.1063/1.5110727.
Synchronization is a phenomenon of the collective behavior of coupled oscillators and involves the detailed interplay of the intrinsic frequencies of the oscillators, the underlying topological features of their interaction network, and external perturbations. In this work we investigate, in the strong coupling regime, the response of a system to external perturbations of its natural frequencies and network modifications. Our investigation relies on two performance measures (one for phases and the other for frequencies) and a spectral perturbation analysis. Given strongly localized perturbations in time, corresponding to the dominant eigenmode of the weighted Laplacian matrix of the network, we present a sufficient condition for the maximization of the system's stability, along with analytical results for the effects of structural perturbations on the system's response. A number of simulations are conducted to illustrate the theory presented.
同步是耦合振子集体行为的一种现象，涉及振子固有频率、其相互作用网络的潜在拓扑特征以及外部扰动之间的详细相互作用。在这项工作中，我们研究在强耦合 regime 下，系统对其固有频率的外部扰动和网络修改的响应。我们的研究依赖于两种性能度量（一种用于相位，另一种用于频率）以及谱扰动分析。给定在时间上强烈局部化的扰动，对应于网络加权拉普拉斯矩阵的主导特征模式，我们给出了系统稳定性最大化的充分条件，以及关于结构扰动对系统响应影响的分析结果。进行了大量模拟以说明所提出的理论。
