Existence And Exponential Stability For Discrete Bidirectional Associative Memory Neural Network Model Cycle Solution

In this paper, the periodic solutions for two classes of discrete-time bidirectional associative memory (BAM) neural networks are discussed. And some sufficient conditions are given for guarantying the global exponential stability and the existence of the periodic solutions for these discrete-time models. The paper consists of four chapters.The historical backgrounds and studying status quo on BAM are briefly addressed in chapter 1. The main content of this paper and related marks are also produced.In chapter 2, some lemmas and concepts about this paper are summarized.By using of semi-discretization technique, we also analyze the discrete-time model of the continuous-time BAM neural network with time-varying delays(The detailed symbols are introduced in Section 3.1).In chapter 3, assuming the boundedness of the signal transmission functions, the existence of the periodic solution for the discrete-time model of continuous-time BAM neural networks with time-varying delays(1) is proved by using M matrix properties and Mawhin's continuation theorem. In Lipschitz condition of the signal transmission functions, the global exponential stability of the periodic solution is gained by using M matrix properties. And an example is given to illustrate the criterions.In chapter 4, assuming the boundedness of the signal transmission functions, the existence of the periodic solution for the discrete-time model of continuous-time BAM neural networks with distributed delaysis proved by using Mawhin's continuation theorem without M matrix properties. At the same time, in Lipschitz condition of the signal transmissionfunctions, the global exponential stability of the periodic solution is gained by using M matrix properties. Also, several useful corollaries are obtained. And an example is given to illustrate the criterions.