Control Of Unstable Equilibrium Points For A Class Of Chaotic Complex Dynamical Networks

The rapid expanding Twitter, the global finacial crisis, a mass of blackout caused by local snowstorm are the complex dynamical networks applications in social life, which is very close to human life. That is why the analysis and control of complex behaviors in complex dynamical networks with a large number of nodes are very important, becoming a veryt hot topic in recent studies.Research methods of complex networks include global control and pinning control. Global control means that all nodes are controlled in order to control the network to a certain state. Meanwhile, pinning control indicates that only some significant nodes are chosen to be conntrolled, making a large-scale complex dynamic network to a target orbit.In this dissertation, the control issue of unstable equilibrium points of a class of chaotic complex dynamical networks is addressed. The main contents are as follows:Firstly, considering the state-coulpling chaotic complex dynamical networks, by using the output control method, we propose a method which can control all the nodes of the network to their equilibrium points. The criteria for choosing control parameters are obtained based on Lyapunov stability theory. Some simulations are given to demonstrate the effectiveness of the proposed method and criteria.Secondly, considering the output-coulpling networks, by using the output control method, we propose a control method to stablize the unstable equilibrium points. The criteria for choosing control parameters are obtained using Lyapunov stability theory.Finally, considering the output-coulpling chaotic complex dynamical networks, the pinning control method is proposed using Lyapunov stability theory, the criteria for choosing the number of nodes and control parameters are given, and some simulations are finished to verify the criteria.