A Class Of Delay Population Development Equation Stability Analysis

In this paper we study a class of population evolution equation with time delay stability analysis. We mainly from the finite delay and infinite delay to study two aspects of population evolution equation’s stability. In finite delay evolution equation with diffusion. And given two parameter plane stability region. In the infinite population evolution equation in the population system is presented the local asymptotic stability condition. In recent years, in chemical reaction, building structure, neural network, microelectronics, ecology etc, there are a lot of research results by evolution equation. In these fields of science, There were a lot of differential equation model, Understanding of these differential equations model will help us to solve the practical problems, For example, lives in the limited resource environment in which predator-prey relationships between species can stabilize development, Based on the model of continuous improvement, Evolution equation also more clearly describe the relationship between population and the ecological balance.In the study of population, We need to consider many factors, For example, a single species population of species in the birth rate and death rate, Species migration and diffusion, And natural disasters such as floods, earthquake, fire and so on population development influence. While discussing a population in a certain period to the development of a steady state,it is tended to be concerned, It is also need to consider the delay factor. Time delay on population plays an important role in the development, Now, study of population development equation has many complete conclusion, But most of the studies are in finite delay study,The discuss for the infinite delay of population development equation of relatively is very few, Therefore, to study the population evolution equation with infinite delay is a concern for many people in recent years.This paper includes three chapters, The first chapter is the introduction, Described the origin and background of delay equations, present development situation, and the main work of this paper.The second chapter discussed the population evolution equation with time delay and with the diffusion of D, the population evolution equation is: In two parameter plane (τ,D) and (τ,r),We discussed the stability of equilibrium solutions and the stability of regional division.The third chapter for the population evolution equation with infinite delay: Respectively from the different kernel functions to study the stability of equilibrium solutions, Including weak kernel function and strong kernel function At last,we discussed the general kernel function,and get general nuclear function system is locally asymptotically stable when the conditions required.