带有时变时滞和非线性耦合的复杂网络同步

Synchronization of nonlinear complex network with time-varying delays

在最近几十年里,复杂网络逐渐成为人们研究的热点,它贯穿了科学和工程的大多数领域.另外,人们在讨论复杂网络时都是假设网络是固定不变的,但是事实上现实世界中很多网络都是增长的,同时还带有时滞,且大多数时滞都是随时间变化的.因此该文研究了耦合和节点都带有时变时滞,以及耦合函数为非线性的动态网络模型的同步问题.首先给出该模型,针对这个新模型,基于Lyapunov稳定性理论和线性矩阵不等式(LMI),论文得到了一些网络同步的充分条件.最后,数值结果表明了方法的有效性.

Complex networks have attracted increasing attention from various fields of science and engineering today. Due to the finite speeds of transmission and spreading as well as traffic congestions, a signal or influence traveling through a complex network often was associated with time delays, and this is very common in biological and physical networks. And most of delays are changing with time. In this paper, we introduced complex dynamical network models with two kinds of time - varying delays in both nodes and coupling item of networks. And then we investigated their synchronization phenomena and criteria. Based on these new complex network models, we derived synchronization conditions in terms of the Lyapunov stability theory and linear matrix inequalities （LMI）. We finally used the results of numerical simulations to illustrate the theoretical results.