Synchronization And Analysis Of Stability For Network Models On Time Scales

The theory of calculus on time scales can reveal the dynamic properties of the systems with the interaction between continuous time intervals and discrete moments.To study the models of networks by applying the theory not only can explore new theo-retical results on time scales,but also can avoid repetitive discussions of the continuous and discrete systems,respectively.In chapter 1,we briefly introduce the background,significance,the current state of neural networks on time scales and the main content and methods.In chapter 2,we analyze the exponential convergence and exponential stability of neural networks based on general exponential properties on time scales.By employing the time scales calculus theory and Lyapunov functional method,we establish sufficient conditions to ensure global and local exponential convergence of the neural networks.The synchro-nization in drive-response networks with discrete and distributed delays on time scales is investigated in chapter 3.Based on the theory of calculus on time scales,Lyapunov functional method and inequality technique,we obtain new sufficient conditions to ensure synchronization criteria which are dependent on boundedness of grainness but independent of the types of delays.Numerical simulations are given to illustrate the effectiveness of our new results.