Qualitative Analysis Of Two Types Of Predator-prey Models

In population dynamic biology,predecessors have done a lot of in-depth research,reaction diffusion equation is the commonly used tool.Studying the relationship between populations can help us propose targeted programs,regulate the relationship between populations,conduct biological control,maintain ecological balance,etc.There are three types of relationship between species:predation,competition and reciprocity.This paper studies two types of predator-prey models,only consider the relationship between predator and prey,do not consider the influence of other factors,and studies some related properties.The main work is as follows:Chapter 1 introduces the research background of biological populations,and some related research results of scholars.Chapter 2 studies a predator-prey model of Leslie-Gower functional response function:This chapter researches the range of positive solutions,the existence and stability of trivial and semmi-trivial solutions,local bifurcation solution,extends the local bifurcation solution to the whole world,proves the existence of the positive solution,the conclusions of this chapter are supplemented and explained by Matlab software.Chapter 3 studies a predator-prey model with Holling-? type functional response function:This chapter obtains a priori estimate of the positive solution,proves the existence of the positive solution by the degree theory.Finally,the correctness of the existence condition of positive solution is verified by numerical simulation.