基于图论方法的耦合系统稳定性分析

Analysis of the Stability and Synchronization of Coupled Systems Based on Graph Theory

随着技术的快速发展,复杂网络研究已经成为生物、物理、数学等学科共同关注的焦点,耦合系统的应用能够很好的描述复杂网络的动态行为,有助于更好的分析系统的结构和响应机制。在耦合系统中,噪声干扰是无法消除的,所以耦合系统的稳定性就显得非常重要。本文以图论分析方法为基础,重点研究带有时变延迟的随机耦合振子的稳定性。

With the rapid development of technology,complex network research has become the focus of attention in biology,physics,mathematics,etc.The application of coupled systems can describe the dynamic behavior of complex networks well,which helps to better analyze the structure of the system and response mechanism.In a coupled system,noise interference cannot be eliminated,so the analysis of the stability and synchronization of the coupled system is very important.Based on the analytic method of Graph Theory,this paper focuses on the stability of stochastic coupled oscillators with time-varying delay.