具有随机扰动和混合时滞的两层异质网络的同步研究

Synchronization of two-layer heterogeneous networks with stochastic perturbations and mixed delays

在现实生活中,很多复杂的系统不是由单个网络来表示,而是由一组相互依赖的网络系统来表示的.本文研究了具有随机扰动和混合时滞的两层异质网络的对应节点的同步控制问题.基于随机微分时滞方程的LaSalle不变原理和Lyapunov稳定性理论,采用牵制控制方法,对部分节点实施控制,给出了实现同步的充分条件.为了降低反馈控制的增益,结合自适应控制的方法,进一步弱化了两层异质网络实现同步的条件.最后,通过数值仿真,验证了理论结果的有效性.

In a real world scenario,several complex systems are represented by a group of interdependent network systems,and not by a single network.This paper focuses on the synchronization control of corresponding nodes in two-layer heterogeneous networks with stochastic perturbations and mixed delays.Based on the LaSalle-type invariance principle and the Lyapunov stability theory,the paper derives sufficient conditions for global asymptotic synchronization by applying the pinning control,which only controls a small fraction of the nodes.To reduce the gain of feedback control,the synchronization conditions of two-layer heterogeneous networks is further weakened by adopting the adaptive control scheme.Finally,the effectiveness of the theoretical results is verified by numerical simulations.