Dynamic Qualitative Study For One Class Of Discrete Neural Network Models With Two Neurons

In this paper, we study the large time behavior of solutions for the following neural network model with two neurons:where n → ∞, λ ∈ (0,1) is a constant, p and q are nonnegative constants, [x]~+ is given byf is the signal function given byIn such a model, we consider not only the interaction of two neurons, but also the message self feedback of themselves. When the neuron is active, it can receive signals of other neurons; when the neuron is inactive, it can restrain other neurons; when the neuron is extremely active, the reflect on other neurons is nothing. In this paper, we divide the values of different parameters in the model. In every different space, we discuss the solutions (x_n, y_n) with different initial values, and analyse the convergent quality of different solutions. There are three chapters in this paper. In chapter 1, we mainly introduces the background, significance and process of this problem as well as some notations which will be used in our paper. In chapter 2, we study the convergence of solution in the situation of p = q = 0. We prove the solution is convergent in such situation. In chapter 3, we study the convergence of solution in the situation of either p = 0 or q = 0. We prove the solution is convergent in the situation of a = 0 and b=1.