Dynamic Analysis Of Several Classes Of Neural Networks On Time Scales

In recent years,with the theory of time scales have been proposed,the dynamic equations of time scales and its applications have aroused wide attention of scholars all over the world.Since the dynamic equations of time scales are more general when we research the system,not only to describe the process of continuous change and discrete change,but also can describe the hybrid process of continuous and discrete.Therefore,the theory of time scales has a wide range of applications in the financial,biological systems,complex networks and engineering applications fields.However,there are few researches on neural networks on time scales,there are still much dynamic behaviors to be further studied,such as stability,multiple periodic solution and synchronization control problems and so on.Based on previous scholars' works,we introduce the theory of calculus on time scales and study the stability,periodic solution and synchronization of the neural networks on time scales.In this paper,dynamical properties of several kinds of networks models on time scales have been analyzed.The main results include three parts: In the first part,exponentially periodic orbits of a class of two-dimension neural networks with N-segment activation on time scales are studied.we guarantee that the model have N2 periodic solutions and the periodic solutions are exponentially stable.In the second part,the complete convergence of a class of simplified background neural networks on time scales are researched,the global attractive set,boundedness and complete convergence for the neural networks are proved.In the third part,synchronization of a class of networks with proportional delays on q-type allowable time scales are studied.The synchronization control problem of networks with proportional delays in discrete time condition are solved.