Dynamic Properties Of A Class Of Delay Binary Artificial Neural Network Model

This paper is composed of two chapters. In Chapter 1, the problems to be studied in this paper, and some basic notations are introduced. In chapter 2, the dynamics of the following model is explored:where x(t),y(t) are the activations of neurons, > 0 is the decay rate, i((i = 1,2) the synaptic transmission delay, / the signal function and is given aswhere c 0 is the connective strength of neurons, a and b are the thresholds. In this chapter, four cases are discussed:for which the periodicities and asymptotic behaviors of the system investigated respectively. A series of sufficient conditions are obtained for the periodicities and asymptotic behaviors of solutions of the model by using step solution of functional differential equation.The results show that initial, delay and threshold are main sources of the behaviors of the dynamics. The trajectories are either synchronized and ultimately periodic or convergent to a desynchronized equilibrium when initial, delay and threshold satisfy some conditions. Our results are new.