具有不确定转移概率的马尔科夫复杂网络的聚类同步

Cluster synchronization of Markovian complex networks with uncertain transition probabilities

研究具有不确定转移概率的马尔科夫复杂网络系统的聚类同步问题,系统模型包含耦合的离散时变时滞和耦合的分布时变时滞.通过充分考虑转移概率的性质和不确定区域的特性,用一个含有较少变量的有效技术代替传统的Young不等式来约束转移率中的不确定项.同时,利用增广李雅普诺夫泛函和具有较小保守性的积分不等式,给出新的依赖时滞和时滞导数上下界的聚类同步准则.最后通过数值仿真验证所提出方法的有效性.

This paper studies the cluster synchronization of Markovian complex networks with uncertain transition rates.This system model contains constant coupled discrete time varying delay and coupled distributed time varying delay. By fully considering the property of transition rates and the characteristic of uncertain domains, a more effective technique in stead of the traditional Young inequality is used to bind the uncertain terms in the transition rates. By applying the augmented Lyapunov-Krasovskii functional and a less conservative integral inequality, new cluster synchronization criteria are obtained, which contains the bounds of the delay and the derivative of delay. The example simulation demonstrates the effectiveness of the proposed method.