Asymptotically Periodicity Of A Class Of Nonlinear Recursive Relationships With Piecewise Continuous Control

Neural network is a new subject with strong comprehensiveness and interdisciplinarity. In the recent twenty years, many domestic and foreign scholars have established a large number of neural network models, Such as the bidirectional associative memory neural networks, Hopfield neural network models,cellular neural network models, and so on.These neural network models have been successfully applied in engineering and technical, Physics, Economics and other areas. In the reseach of neural network, dynamic propertives of time-delay neural network, such as stability, instability, oscillation and chaotic behavior have recently become important topics, and attracted a lot of attention,It is well known that everyone, most of the artificial neural network model can be described by the qualitative theory of differential equation, difference equation, As a result, the design the application of qualitative theory the differential equation, differential equation and on the artificial neural network play important roles. At present, there are a lot of results about the existence of periodic solutions for neural network model, stability and attractability have a lot of research results. But the nonlinear neural network model in the study of asymptotic properties of solution is relatively small, especially for the a piecewise continuous control of the research achievements of neural network model is less.This paper mainly studies the following form of nonlinear difference equation Where{an}n=0∞,{bn}n=0∞ are 2k+1- periodic sequences with ai ∈ (0,1), bi= 1-a,i,i= 0,1,…,k. f satisfies which λ ∈ (0,+∞). we can put the equation(1)can be considered as nonlinear neural network model.By the transform xn(i)= x(2k+1)n+i,(n,i) ∈ N×{0,1,…,2k} ∪{-1}×{2k-1,2k}, the above equation can be converted into the following 2k+1-dimensional autonmous dynamical systemThis paper is divided into three chapters:The first chapter, introduction part, mainly states the research background and current situation of the development of neural network, and introduces some related research results of neural network model and main work of this article;The second chapter, we introduce some basic definitions and related symbols;The third chapter, we mainly research the asymptotic periodic solution when the thresh-old valuelies in different value range. By analyzing(2), the completely asymptotic behavior of (1) is obtained.