Selection Of Minimum Wave Speed For Some Class Of Lotka-Volterra Competition Models

As a research hotspot,reaction diffusion equations are widely used in various mathematical models of real life.Examining the various characteristics of traveling wave solutions of reaction diffusion equations helps to make better predictions of actual problem models in real society.Regulating and processing schemes,and the mechanism of selecting the minimum velocity of traveling wave solutions,have naturally become one of the leading topics in the study of reaction-diffusion equations.This paper presents two types of representative reaction-diffusion equation models,which use the upper and lower solutions to minimum wave velocity was studied and some new conclusions were obtained.This article is divided into three chapters.In Chapter 1,we introduced the research background of this article,the current status of domestic and foreign research,and the main content and innovations of this article.In Chapter 2,we study the minimal speed(spreading speed)selection mechanism of traveling waves to a periodic diffusive Lotka-Volterra model with monostable nonlinearity.The method of upper and lower solutions pair is applied to establish the existence of traveling waves.We prove that the nature of nonlinear selection is to find a lower solution pair with the first species decaying in a faster rate.By novel constructions of various upper and lower solutions,we obtain a number of new results on the minimal speed determinacy.Numerical simulations are carried out to illustrate all of our discoveries.In Chapter 3,this part is based on Chapter 2 to further explore and analyze.In this part,we study a two-group competition model for nonlocal diffusion in a class of classical Lotka-Volterra systems.Firstly,after transforming it into a cooperative system,the upper and lower solutions are used to study the selection mechanism of the minimum wave velocity of monotone traveling wave and traveling wave diffusion as linear or nonlinear,and the influence of competition coefficient on its speed selection mechanism is obtained.