Outer Synchronization Between Two Complex Networks With Nonidentical Topological Structures And Time-varying Delays

Many systems in nature can be described by complex networks, such as Internet,human nevous networks, metabolic networks. Research on complex networks is verysignificant as the application field of complex network is very broad.Firstly, this thesis introduces the model of diffusively coupled dynamical networksand theoretically analyzes the synchronization of two networks with nonidentical couplingconfigurations under the application of adaptive controllers. When part of the topologicalstructure of driving network is the same as that of response network, the contronllers canbe simplified. In the special case of the two matrixes are equal, the controlles become onlythe last variables. Several examples for illustrating outer synchroniazation are given.Secondly, the article introduces the model of linearly coupled complex networks withtime-varying delay and the feedback adaptive controllers are designed for the global outersynchronization of the drive-response network system. Giving the numerical examples, weobtain that the controllers are highly robust against uncertain parameters, such as nodedynamics, coupling matrix and time delays.Finally, the thesis introduces the model of diffusively coupled complex networks withtime-varying delay under the application of pinning controllers. The parameters of thenetwork model are designed based on Lyapunov functional method. Simulations are givenfor100nodes of the BA scale-free network showing the effectiveness of the proposedmethod. Then a feedback controller is proposed by pinning control method to get the outerand inner synchronization of the general drive-response networks. Based on Lyapunovfunctional method, the coupling strength and the conditions of the uncoupled dynamics aredesigned. At last, Simulations are given for100nodes of the WS small-word networkshowing the effectiveness of the proposed method.