The Research On Asymptotic Behavior Of Solutions To A Type Of Two-neuron Neural Network On Time Scales

In this paper, we make good use of the basic theory of dynamic equations on time scales, and consider the asymptotic behavior of solutions to a type of two-neuron neural network with delay. Time scales is put forward by doctor Stefan Hilger in his doctoral dissertation, and its goal is to unify the kinetic properties of the kinetic equation under the condition of the discrete and the continuous. The research on kinetic equations on time scales discovers the difference of kinetic equations under the condition of the discrete and the continuous. The system can be regarded as the unification of an artificial network model of two neurons under the condition of the continuous and the discrete. Therefore, to analyze problems by employment of new theory on time scales could provide available methods for the research of neural network.The paper consists of three chapters. In chapter one, We firstly introduce the problem's background, importance and what's going on, then we introduce some basic knowledge on time scales which is necessary in this paper. We especially take into account the asymptotic behavior of solutions to the model when signal function is with McCulloch-Pitts type in the second chapter. As for threshold of the signal function, we divide it into three cases. Our analysis shows that once the signal function and the threshold are different, the kinetic behavior of solutions to the system shows corresponding different properties. However, these are in accord with the reality. In the last chapter we study the asymptotic behavior of solutions to the model when the signal function is a nonlinear constant function. As far as threshold of the signal function, we divide it in detail as well. Although the signal function is a two-linear constant function, variable can come from one of the two intervals when the function value is zero. Compared with chapter two, it is more complicated especially when the value of threshold is 1. We have got some interesting results about the asymptotic behavior of solutions.