非线性动力学网络同步的纯图论方法
A (Purely) Graph-Theoretic Approach to Synchronization of Nonlinear Dynamical Networks
中文总结 AI 辅助
该研究针对大型非线性动力学网络同步问题，提出纯图论框架，通过直接从有向图计算耦合强度，复杂度为O(n³)，可在现有方法不可行时实现网络同步。
中文摘要 AI 辅助
同步非线性动力学网络通常需要求解矩阵不等式或详细的系统模型，这些方法对于大型网络失效。本文提供了一种简单解决方案：一种纯图论框架，仅对动力学使用单个类Lipschitz界。耦合强度直接从有向图计算，完全绕过不等式求解器。该方法在现有方法因连通性模式不可行的情况下成功。它对每个强连通分量仅检查n-1条有向路径，而之前检查n(n-1)/2条无向路径，实现O(n³)复杂度。结果表明，可利用网络连通性同步一大类非线性动力学网络。
英文摘要
Synchronizing nonlinear dynamical networks typically requires solving matrix inequalities or detailed system models, which fail for large networks. This paper offers a simple fix : a purely graph-theoretic framework using only a single Lipschitz-like bound on the dynamics. Coupling strengths are computed directly from the digraph, bypassing inequality solvers entirely. The method succeeds where existing approaches encounter infeasibility due to connectivity patterns. It examines only $n-1$ directed paths per strongly connected component versus $\frac{n(n-1)}{2}$ undirected paths before, achieving $O(n^3)$ complexity. Results show network connectivity can be exploited to synchronize a large class of nonlinear dynamical networks.
