具有切换拓扑结构的非恒等节点复杂网络同步化判据(英文)

A synchronization criterion for dynamical networks with non-identical nodes and switching topology

网络拓扑结构与节点动态在复杂网络的同步化过程中起着关键性的作用,针对具有切换拓扑结构与非恒等节点的同步化问题还没有非常有效的判据.本文研究了具有切换拓扑与非恒等节点的复杂网络同步化问题,针对非恒等节点不存在公共平衡解的情况,选取所有节点的平均状态作为同步化目标,并在此基础上建立起误差动态方程.基于所有外部耦合矩阵可以同时三角化的条件下,构建了低维系统的公共Lyapunov函数,提出了在误差向量范数有界意义下的复杂网络全局同步化判据,保证系统在任意切换策略下实现复杂网络的同步化.最后通过数值仿真验证了结果的有效性.

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for dynamical networks with non-identical nodes and switching topology. This paper studies the synchronization problem of a complex network with non-identical nodes and switching connection topology. Considering the general case where no common equilibrium solution is assumed to exist, we select the average state of all nodes as the target of synchronization and establish the dynamical error equations. Under the condition of simultaneous triangularization of the outer connection matrices, a common Lyapunov function is constructed by those of several lower dimensional dynamic systems, a global synchronization criterion in the sense of boundedness of the maximum state deviation between the nodes is proposed under arbitrary switching topology. Finally, numerical simulations are provided to show the effectiveness of the results.