Stability and synchronization of complex networks composed of dynamical nodes with discontinuities

随着通信、计算和互联网的快速发展，使我们能够收集和分析大量的信息，近年来人们对复杂网络的兴趣越来越大。一个复杂的网络是一个被称为节点的相互连接的动态单元的大集合。每个节点都是具有特定行为的动态系统。有许多自然和人为的复杂网络的例子，如遗传调控网络、通信网络、交通网络、电网、社会关系网络和万维网等。由于其耦合结构，复杂网络可以表现出与单个节点完全不同的复杂动态。因此，研究复杂动态网络的集体动力学行为，如稳定性和同步性，以及在复杂网络中发生的其他相关过程的性质，如疾病和信息的传播，是非常重要的。

With the rapid development of communication, computation and the Internet, which allow us to gather and analyze large amount of information, there has been a growing interest in complex networks in recent years. A complex network is a large set of interconnected dynamical units called nodes. Each node is adynamical system with specific behavior. There are numerous examples of natural and man made complex networks such as genetic regulatory networks,communication networks, transportation networks, electrical power grids, social relation networks, and the World Wide Web, among many others. Acomplex network can exhibit complicated dynamics that may be totally different from those of a single node due to its coupling architecture. Thus it is veryimportant to study the collective dynamical behavior, such as stability and synchronization, of complex dynamical networks as well as properties of otherrelevant processes that take place in complex networks such as the spreading of diseases and information.