The Dynamical Analysis Of Several Neural Networks On Time Scales

Neural network is a highly complicated nonlinear dynamics system,which has rich dynamical behavior.In recent decades,the theory and application of neural networks has attracted the wide attention of many research and experts.The theory of time scales has unified the dynamic property of the differential system under the continuous and discrete situation.Therefore,research the dynamic character of neural network model on time scale has important theoretical significance and application value.In chapter 1,we outlined the dynamical research of neural network,the current state of time scale neural network and the main content and methods.In chapter 2,we discuss the existence of periodic solutions for neutral-type neural networks with delays on time scales.Some new sufficient conditions are established to show that there exists a unique periodic solution by the fixed point theorem and the contraction mapping principle.In chapter 3,we investigate Wilson-Cowan neural networks with periodic coefficients and delay on time scales.By applying the theory of calculus on time scales,the contraction mapping principle and Lyapunov functional,we obtained the existence,uniqueness and exponential stability of periodic solution to the considered system.Genetic regulatory networks with delay on time scales is considered in chapter 4.Some sufficient conditions for the existence and exponential stability of a unique equilibrium of genetic regulatory networks are established.The approaches are based on constructing Lyapunov functionals and the well-known Brouwer's fixed point theorem.