Dynamic Synchronous Control Of Complex Network With Clustering Delay’s Reach

Recently, complex network has become an important interdisciplinary field, whichattracts more and more researchers in physics, biology, mathematies, computer, ete. Theresearch on synchronization problem of complex network has become one of the hotresearches in control field, and it is one of strategic issues of science and technology in the21st century. Complex network’s entirety dynamical behaviors and the whole network’stopology structure has become wide attention in the complex network research. The mostimportant research content in complex network is pinning controll and stability analysis.In the real world, many networks have obvious community structure. The basicfeature is the node in the same community with high connection degree and the node inthe different community with low connection degree. In this paper, the related theories ofcomplex network system have been proposed. Several complex clustering network modelsand theirs synchronization control designs are put forward. The article main researchcontents are as follows:First, the basic model and the main statistical characteristics of complex network aredescribed, research was introduced briefly the basic principle of synchronous control andstability as well as the techniques and methods used and the research purpose of thissubject is pointed out.Second, the complex clustering network with nonlinear dynamical node isinvestigated. Respectively from the topology directed and undirected two aspects problemdescription and synchronization design scheme is put forward. Combining with linearfeedback control, adaptive control and pinning control method, using the Lyapunovstability theory, some sufficient conditions for the synchronization are derived andnumerical simulation examples are provided to verify the correctness and effectiveness ofthe proposed scheme by Matlab.Third, the complex network model with time-varying coupling and time-varyingdynamic node is investigated, respectively from two aspects of coupling method is linear and nonlinear proof of synchronous control method is put forward. The internal andexternal coupling matrixs of the network are time-varying. Combined with adaptivecontroller and pinning control method, using the Lyapunov stability theory, somesufficient conditions for the synchronization are derived, numerical simulation examplesare provided to verify the correctness and effectiveness of the proposed scheme by Matlab.Finally, analysis nonlinear directed coupled complex networks, nonlinear undirectedcoupled complex networks and linear coupled complex networks and complex networksof nonlinear coupling both in synchronization control process and the simulation results ofsimilarities and differences.