具有瞬时耦合及通讯时滞的调和振子同步动力学

摘要

针对具有局部瞬时耦合及通讯延时的调和振子动力网络系统,给出了一种分布式同步算法.分别在无向固定拓扑和切换拓扑两种情形下给出了同步态的解析表达式,以及耦合系统的解析解,并给出了一些一般而简单的同步化准则.结果表明网络化的调和振子在比较弱的瞬时网络连通条件下,可以达到同步状态.数值模拟表明所给理论结果的正确性和有效性.%This paper presents a distributed synchronization algorithm in undirected networks of coupled harmonic oscillators having diverse communication delays under local instantaneous interaction. Some generic yet simple criteria for such algorithm over, respectively, undirected fixed and switching network topologies are given as well as the analytical synchronization states and the analytical solution of the coupled system. It is shown that the networked delayed harmonic oscillators can be synchronized under mild instantaneous network connectivity. Subsequently, numerical simulations illustrate and visualize the effectiveness and feasibility of the theoretical results.