Dynamics of some neural network models

Abstract

This Ph.D. dissertation consists of four chapters and mainly deals with the dynamics of several neural network models described by delay differential equations, difference equations and stochastic differential equations. -- In Chapter 1, some background of neural networks and the motivations of this work are briefly addressed. -- In Chapter 2, Liapunov functional method and the theory of monotone dynamical systems are employed to obtain some delay independent and delay dependent stability results for the general continuous-time Cohen-Grossberg neural networks with distributed delays. Detailed local stability and bifurcation analysis are also given in this chapter for the bidirectional associative memory (BAM) neural networks with and without self-connections. -- Chapter 3 is devoted to the study of discrete-time neural networks with delays. Specifically, we first derive some global stability results for the discrete-time neural networks with variable delays and then investigate the capacity of the discrete-time BAM neural networks by giving the number of all possible stable periodic solutions. -- The stochastic neural networks are studied in Chapter 4, in which some criteria for the almost sure exponential stability, mean square exponential stability are established for stochastic Cohen-Grossberg neural networks with and without delays.