Dynamic Analysis For Several Delay Neural Network Models Of Difference And Differential Equations

The dynamics of neural network, which has been applied widely, is the foundation of application and design. Considering that there is time-lag in the transference of information between neurons in the neural network, the neural network models described by difference equations and differential equations should contain delays. Due to the shortage of efficient tool and method in the qualitative analysis of large delay difference and differential equations , while the dynamical study of small delay neural network models can provide useful method and tool to investigation of large network, so it is meaningful that we study the dynamics of small difference equations and differential equations neural network with delays. This dissertation mainly explores the dynamics of solutions of several delay small neural network models described by delay differential equations and delay difference equations, including the convergence, periodicity and stability of equilibrium solutions of the models.This dissertation is consists of four chapters.As the introduction, in Chapter 1, the history, background of neural networks and main reserch contents of the dissertation are briefly addressed.In Chapter 2, the dissertation discusses the convergence of solutions and the existence of asymptotically stable periodic solutions of a class of delay difference equations with piecewise constant nonlinearity by means of the inequality skills, the iteration of a one-dimensional map and fixed point theorem, In a given space of initial function, the convergence of solution of the model is proved for some different scopes of signal function threshold; a existence condition which can guarantee the existence of a asymptotically stable periodic solutions of the model is obtained.In Chapter 3, the dissertation improves a discrete-time difference neural network model of two neurons, and introduces two different nonlinear discontinuous signal functions which display obviously meaning. In a given space of initial function, the convergence of solution of the improved model is obtained for big and critical threshold of signal functions respectively; for small threshold, a existence theorem of a asymptotically stable synchronized periodic solutions is proved by means of the iteration of a one-dimensional map and fixed point theorem.In Chapter 4, the dissertation investigates the linear stability of the steady-...