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

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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.