Yuen Shen | Applied Math, University of Waterloo
Impulsive synchronization of general complex dynamical networks
Complex dynamical networks exist in all fields of sciences and humanities, and have been intensively studied over the past decades. Common examples include World Wide Web, Internet, food webs, social networks, neural networks etc. Particularly, one of the most significant phenomena, which happens within a complex dynamical network, is the synchronization of all dynamical nodes. Many real-world problems have close relationships with network synchronization, such as the synchronous information exchange in the Internet, and the spread of an epidemic or computer virus. Lyapunov function direct method and several control schemes have been introduced to realize network synchronization, such as impulse control, adaptive control, pinning control etc. Among these approaches, impulsive synchronization method is effective and relatively easily realized. It allows synchronization of a complex network by small impulse signals being sent to the receive systems at certain impulsive moments, which can reduce the information redundancy in the transmitted signal and improve the security and robustness against the disturbance.
In this talk, a complex dynamical network model with complex-valued nodes is considered, the impulsive control scheme and synchronization criteria are given, the numerical simulation result shows that previous synchronization criteria for networks consisting of real-valued nodes can be revised and extended to complex space.