With Three Sections Of Constant Continuous Signal Transfer Function Of The Discrete Neural Network Model Of The Dynamics

This thesis has studied the dynamic features of a class of the discrete-time neural network model of two neurons,such as the convergence and periodicity and etc .The function of the neuron signal transmission in this model,which belongs to three piecewise constant argument,indicates the following charactersif the signal of one neuron on the network is active between a and b ,it will produce invariable encouragement effect on another neuron;If the signal of one neuron is lower than a ,it will produce invariable restrain effect on another one,If the signal of one neuron is higher than b,it will produce no effect on another one. This sort of model has its practical significance.First,the standardization is applied to the the study.ln order to analyse the dependence of the initial value of the model's solutions,the plane is divided into 9 areas by the activation of nerons.Then the convergence and periodicity of the model solutions have been studied in three situations by means of the step method: (l)a> 1, (2)0 < a < 1 ,(3)a < 0.Detailed discussions are processed about parameter b's possible value and all kinds of initial value in the parameter a's each situation. A series of sufficient conditions have been obtained for the convergence and periodicity of sulotions of the model. These conditions show that the convergence and periodicity of solutions depend on the parameter a and b,and on the range of the initial value .When a > 1 ,the solutions will entirely converge to point (-1,-1) ,When a = 1 ,the solutions will converge to point (-1,-1) or (l,l),but there will be no periodic solution.When 0 1, the solutions will entirely converge to point (1,1); When a<-1 and -1