Exponential Synchronization Of Complex Spatiotemporal Networks With Topological Switching Characteristics

Nowadays,complex networks are more and more widely used in related fields,especially the synchronization of complex networks is very important for people's life and social development.With the deepening of the research on the synchronization of complex networks,the research on the synchronization of complex networks with topology switching characteristics has shown particularly outstanding practical value.In this thesis,the exponential synchronization problem of complex spatiotemporal networks with topology switching characteristics is studied.The specific research contents are as follows:The exponential synchronization problem of discrete uncertain spatiotemporal networks with topology switching characteristics is researched.Based on the stability theory,the Lyapunov function with exponential form is constructed and the synchronous controller is designed,and then the synchronization condition of the spatiotemporal network is obtained.Meanwhile,the unknown parameters of the network are identified effectively by designing the identification law of the unknown parameters.Finally,we use phase-conjugate wave spatial expanded system as the nodes of the network to simulate,and the feasibility of the synchronization scheme and the effectiveness of the controller is verified.The exponential synchronization problem of continuous uncertain spatiotemporal networks with topology switching characteristics and time-lag is researched.By constructing a special Lyapunov function,we determine the exponential synchronization conditions for complex spatiotemporal networks,and the structure equation of the network synchronization controller is also determined.In addition,the unknown parameters of the network are identified effectively by designing the identification law of the unknown parameters.In the numerical simulation,we choose the Predator-Prey spatiotemporal chaotic system as the network node to simulate,and the results verify the correctness of the theoretical analysis.The synchronization technology designed in this thesis is more practical,because it takes into account the actual factors such as the different numbers of nodes between networks and the existence of time delay.At the same time,by constructing Lyapunov function with exponential form,the synchronization rate of the network can be effectively adjusted,and the synchronization conditions obtained do not include the coupling matrix term of the network,which eliminates the influence of thetopological switching characteristics on the synchronization process and makes the synchronization performance of the network more stable.