Research On Synchronizatin Issue Of The Complex Neural Network

With the research of complex network, the complexity of network systems and its synchronization has been the hot topic, many scholars in various fields have been widely concerned about the complexity of network systems and their behavior.Synchronization of complex networks can portray the mathematical mechanism of the realistic network model truly. It not only can be applied to the nonlinear science, but also be applied to medical, communications, economic and other fields. So it have good prospect in application.In this paper, the basic concept and several basic models of complex networks is described. H-R neural network as the research object; we mainly study the complete synchronization of the weighted network, phase synchronization and adaptive time-delay synchronization based on stability theory, matrix theory and control theory. Furthermore the adaptive time-delay synchronization project was applied to secure communications systems.Firstly, the research progress of the complex network synchronization and the basic concept are described. Further the model of the weighted NW small-world networks is established when the topology of the network is given in this paper. Then the sufficient condition for synchronization in weighted networks is obtained by stability theory and matrix theory under the conditions of the weight is fixed. Moreover, the H-R neurons network is used to verify its feasibility via numerical simulation. Finally, the smallest coupled strength is obtained when connection probability is existent. Secondly, the phase synchronization is studied, the model of phase synchronization -Kuramoto is presented, and the relation between the topology of small-world network, the coupling strength and the phase synchronization of the H-R neural network are discussed. Moreover, a more general adaptive time-delay synchronization method is presented based on the Lasalle invariance principle. The feedback control strength of this method not only depends on the initial position, but the time-delay and coefficient of feedback control. Moreover, the H-R neurons networks are applied to verify its effectiveness and feasibility. At last, the method is applied to secure communications and simulation shows it can achieve the good performance.