Dynamic Analysis Of A Diffusive Competitive Model In A Evolving Domain

Survival competition is a common phenomenon in nature.The competition between species and the variation of environment both will lead to the change of population size.However,the living planet report 2020 released by WWF in 2020 shows that the number of mammals,birds,fish,amphibians and reptiles in the world decreased by 68%from 1970 to 2016 on average.We need to understand the factors affecting the survival and extinction of the population,analyze the trends of population development and provide a theoretical basis for the utilization of biological resources.This paper concerns the classic Lotka-Volterra competition model with diffusive effect and studies the impacts of two different evolving domains,including the growing domain and the periodic evolving domain,on the long-term behavior of populations.During the formulation of model,the regional evolution rates are defined to reflect how the domains evolve,and the ecological reproduction indexes are established as thresholds.The long-term behavior of competitive population in such habitats will be clarified.This paper includes the following four chapters.The first chapter mainly introduces the background and significance of our study.It includes the historical background and research status of the two species competition model,the significance and feasibility of the discussion about population model in the evolving domains and the arrangement of this paper.In the second chapter,we study the two species competition model in a growing domain.The ecological reproduction indexes connected with the eigenvalue problem are established to explain the influence of the growing domain on the living state of the two competitors.With the basis of theoretical analysis,we use MATLAB to simulate the long time behavior of two competitive populations in a growing domain and verify the theoretical results with the graphs drawn.In the third chapter,we discuss the two species competition model in a periodically evolving domain.After linearization at the trivial solution,we derive the characteristic equation and give the threshold analysis.We clarify how the periodic evolution of the region will affect the survival and extinction of the two competing species,and give some biological explanations combined with numerical simulations.At last,we sum up the main achievements of this paper and discuss the problems could be considered and studied in the future.