Stability Analysis Of Several Classes Of Delayed Neural Network Models

In this thesis,the dynamic behaviors of solutions is considered for the following three kinds of neural network models;a tri-neuron network a stochastic delayed Cohen-Grossberg neural network and a class of stochastic delayed cellular neural networks A set of stability results for such neural network models are derived by employing Brouwer’s fixed point theorem,inequality analysis and the semimartingale convergence theorem.This paper consists of four chapters.In Chapter one,the background of neural networks are briefly addressed.We study the stability of the model（1）with time varying delays in de-tail in Chapter two.In Chapter three,we make a further investigation of model（2）;with the help of Lyapunov function and the Dini derivative of the expectation of V（t,X（t）） "along" the solution X（t）of the model（X（t）=（x₁（t）,…,x_n（t））^T）,a set of novel suf-ficient conditions on pth moment exponential stability are given.In Chapter four,using the suitable Lyapunov functional and the semimartingale convergence theorem,we obtain some sufficient criteria insuring the almost sure exponential stability of model（3）.The conditions in our results are in term of the parameters of the connection matrix and activation functions and are independent of all delays,which may possess highly im-portant significance in some applications.For instance,they can be applied to globally exponentially stable neural networks and easily checked in practice by simple algebraic methods.