Existence Of Periodic Traveling Waves In Discrete Neural Networks With Polynomial Reactions

Neural network is a kind of mathematical models which use synapse like structure to process information. It is widely used in communications, radar, medical engineering, image processing and some other fields of study. Recent years, the study of the theory and application of continuous neural networks developed quickly, while the study of discrete neural networks developed slowly. It appeared some research results in the wave solution of discrete neural networks, but all these are based on1+1dimensional space and there were no results discussed in2+1or multi-dimensional space. This paper will discuss the existence of periodic traveling waves in discrete neural networks with polynomial reactions.This paper consists of four chapters. In chapter one, we discuss the topic research signifi-cance and the present situation as well as the work of this paper. In chapter two, the definition of the three periodic wave solutions and some concepts are given,the existence of wave solu-tion of the discrete neural networks are discussed. It shows that the existence problem of wave solutions of the model can be transformed into the corresponding existence problem of wave solutions of partial difference equations, and the relations between this model and other partial difference equations are also established. In chapter three, some properties of doubly periodic are demonstrated, and the sufficient conditions of the existence of the wave solution are established. In chapter four, the existence result of periodic wave solutions are proved by analysis method.