摘要
复杂网络无处不在,同步是自然界中广泛存在的一类非常重要的非线性现象.过去10年,人们对复杂网络的同步开展了系统而深入的研究,包括恒等同步、广义同步、簇同步以及部分同步等.上述大部分结果中对同步速度的刻画往往是渐进的,只有当时间趋于无穷的时候,网络才能实现同步,而对于网络能够在多长时间内可以实现同步却知之甚少.作者以几类典型的非线性耦合的复杂动态网络为例,深入探讨了复杂动态网络的有限时间同步的规律.具体而言,基于上述几类典型的复杂动态网络,证明了在某些合适的条件下,网络能够在有限时间内实现精确同步.此外,用一个典型的数值仿真实例验证了上述有限时间同步的准则.有限时间同步有效地避免了网络只有在无穷时刻才能实现同步的问题,对网络同步的实际工程应用具有基本的现实意义.
Complex networks are everywhere. Synchronization is a very important nonlinear phenomenon which universally exists in nature. Over the last decade, many researchers have further investigated the synchronization of complex dynamical networks, including identical synchronzation, clustering synchronization, partial synchronization, and so on. The characterization of synchronous speed of complex dynamical networks in most known results is asymptotic. That is, complex networks can realize synchronization only when the time t tends to infinity. However, there are few results reported on how long complex networks can reach synchronization. Based on two kinds of typical complex dynamical networks with nonlinear coupling, this paper will further explore the finite-time synchronization of complex dynamical networks. In detail, under some suitable conditions, it is proved that the above complex dynamical networks can realize accurate synchronization within finitetime. Moreover, a typical numerical simulation is then given to validate the effectiveness of the proposed criteria for finitetime synchronization. It should be especially pointed out that the finite-time synchronization sucessfully overcomes the difficulty of infinite synchronous time. The above results have some important practical meaning for the real-world engineering application.
出处
《系统科学与数学》
CSCD
北大核心
2009年第10期1419-1430,共12页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(60821091
60772158)
973项目(2007CB310805)资助课题
关键词
复杂网络
同步
有限时间
无向图
非线性耦合.
Complex networks, synchronization, finite time, undirected graph, nonlinear coupling.
