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 a*dynamical 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. A*complex network can exhibit complicated dynamics that may be totally different from those of a single node due to its coupling architecture. Thus it is very*important to study the collective dynamical behavior, such as stability and synchronization, of complex dynamical networks as well as properties of other*relevant processes that take place in complex networks such as the spreading of diseases and information.*******In this research program, we will mainly focus on those complex networks composed of dynamical units with switching or jump discontinuities. Such*dynamical units include switched systems, impulsive systems, or more generally hybrid systems, which are often used to model practical systems*having certain embedded intelligence (sometime called the smart systems). Our objectives include: (i) to develop stability theory and robustness of such*complex networks;(ii) to establish various synchronization criteria of complex networks; (iii) to develop effective impulsive control and hybrid control*methods for stabilization and synchronization of complex networks; (iv) to develop efficient and reliable computational algorithms for computational modeling and simulation of complex networks; (v) to apply the obtained methods to practical problems such as disease transmission and spreading over social networks.*The outcomes of this research program will result in new stability and robustness results, new synchronization criteria, effective impulsive and hybrid*control methods, efficient computational algorithms for modeling and simulation of complex dynamical networks.*******The outcomes will enhance Canada's reputation for leading edge research and facilitate opportunities for international collaboration. We expect to publish several top quality papers per year in prestigious international journals. This research program will also provide an excellent opportunity for training graduate students and other highly qualified personnel.