Invasion Speed And Minimum Wave Speed Of Two Kinds Of Predator-prey Models

In recent years,more and more attention has been paid to ecological problems.Different populations influence each other and are indivisible.Therefore,the population model has an important role in ecology.And the predation relationship is one of their basic relationships.So the investigations on predator-prey problems attract more and more attention.This article mainly studies the invasion speed and the minimum wave speed of two kinds of predator-prey models.In chapter 1,we mainly describe the research background of the predator-prey model and the current research status at home and abroad.And the main contents of this paper have been described.In chapter 2,we mainly give various theorems and lemmas which are used in this manuscript.In chapter 3,we mainly study the invasion rate of a predator-prey model with two predators and one predator.Firstly,the equilibrium point of the model without predators has been calculated,and the initial conditions of the model are given.Then,the invasion speed of the model is obtained by using the strong maximum principle and the comparison principle.In chapter 4,we mainly study the invasion speed of a predator-prey model with two predators and one predator with Holling type ? functional response function.Firstly,the equilibrium point and initial conditions of the model are given.Then according to the maximum principle,comparison principle,compactness theorem,L'Hospital rule and other theorems,the invasion speed of this model is obtained.In chapter 5,we mainly study the minimum wave speed of connecting the point)0,0,0(and the equilibrium point without predator.Firstly,we give the definition of the upper and lower solutions of the model,and Schauder fixed point theorem is applied to prove the existence of solutions of the model.When the wave speed is greater than or equal to the invasion speed,the upper and lower solutions suitable for all speeds have been constructed for the model.Secondly,the existence of traveling wave is derived by using the idea of rectangular contraction.Finally,we obtain when the wave speed is less than the invasion speed,the model does not meet the conditions of the positive solution.The minimum wave speed of the model is obtained.In chapter 6,the main research conclusion is summarized,and gives some directions of further research.