Study On Synchronzation In Complex Dynamical Network

Complex network has caused a considerable interest in the study of science and engineering, with the rapid development of computer science and network theory, which becomes a new researching focus in recent years. The so-called complex network is a big network which is provided with complex topology and behavior, and is a map which is comprised of brims'mutual joints by a great deal of nodes. Because a lot of complex networks exist in our daily life, such as Internet, WWW, metabolic network, social network, energy-supplying network, transportation network, information network, finance network and so on, all of those are greatly associated with daily life. As far as physician, one of the terminal goals about researching complex network is to understand the impact on physical process which is caused by network topology. Synchronous phenomenon also is an important researching task.The conceptions of complex network, modeling of complex dynamical network, and its analysis and control are introduced in the thesis.Correlative researching outcomes recently at home and abroad concerning synchronous issues about complex dynamical network have been analyzed, the impacts on synchronism dynamics which are produced by network structure have been discussed. This thesis has clearly analyzed synchronous issues of various types of complex networks, which mainly contain synchronization of linear coupling complex dynamical network, synchronization of nonlinear coupling complex dynamical network, generalized synchronization of time-changing complex dynamical network, synchronization of stationary time-delaying complex dynamical network, and part synchronization of time-changing and time-delaying complex dynamical network. Based on Lyapunov function, mathematic inequality, linear matrix inequality technique and theory, some synchronous condition which those multifarious types of complex networks need were derived. Given the conservation of linear matrix inequality, and the simplicity of form, this thesis solves the numerical value about the mentioned LMI condition by LMI workbox of MATLAB software, and numerical simulation is given to prove the effectiveness of this method.