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

近年来，随着通信、计算和互联网的迅速发展，人们可以收集和分析大量的信息，对复杂网络的研究越来越受到人们的关注。一个复杂的网络是一个大型的相互连接的动态单元称为节点。每个节点都是具有特定行为的辅助系统。有许多自然和人造复杂网络的例子，如遗传调控网络，通信网络，运输网络，电网，社会关系网络和万维网等。复杂网络由于其耦合结构，可以表现出与单个节点完全不同的复杂动力学行为。因此，研究复杂动力网络的稳定性、同步性等集体动力学行为，以及疾病传播、信息传播等复杂网络中相关过程的性质具有重要意义。

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.