Analysis On Outer Synchronization Control For Some Classes Of Complex Dynamical Networks With Time Delays

Complex network is a vital tool and method to describe and understand complex systems. In recent years, it has attracted increasing attention and widely used in various fields of sociology, biological sciences, physics, engineering science and so on. At present, the discussions mainly focused on the study of synchronization control for complex dynamic network. In this paper, we give several outer synchronization criteria under the factor of time delay and controllers through the control theory and mathematical analysis method, the main work is as follows:Firstly, we studied the synchronization control for a class of complex dynamical network with time-varying coupling delay. At first, we gave the basically investigative model and constructed the drive-response network system. Then, by designing appropriate sampled-data controller, we get the error system of drive-response networks.Thus, we can transform the outer synchronization between two systems into the stability problem of the error system, and give a new criterion for judging the stability of the error system. Features of this paper is using the stability theory for functional differential equations, constructing a suitable Lyapunov function, and using the Jensen inequality, Wirtinger inequality to deal with the derivative of the function V and joined the free-weighting matrix to make the diagonal elements of the matrix to be nonzero.Secondly, we studied a class of complex dynamic network with time-varying delay via output coupling. In the model, the nodes are coupled via the output function. Thus,we consider both the coupling terms with delays, also consider the coupling term without delay. Using the same control theory of previous chapter, we re-constructed Lyapunov function and gave an outer synchronization criterion of complex dynamic network with time-varying delay via output coupling.Finally, we studied the outer synchronization control of two complex networks with different dynamic nodes. Unlike the previous model considered, we assumed that the drive network and the response network has different dynamic node. In this section,we designed a pinning controller, by analyzing the stability of the error system, a kind of anti-phase synchronization method is proposed. The feasibility of our theorem is proved by the tool box of MATLAB.