Dynamic Analysis Of A Diffusive Predator-Prey System On Evolving Domains

Predation is a common phenomenon in nature,and scholars usually establish population models to study the interaction between predator and prey.One type of work on ecological models is to restrict the habitat to a fixed area.In fact,the survival environment of a population is influenced by many factors,among which we only consider habitat changes over time.Therefore,we study the dynamics of predator-prey systems on evolving domains to provide some theoretical basis for promoting species diversity and the utilization of biological resources.In this paper,we introduce a Lotka-Volterra predator-prey system with Holling-II functional response functions.The dynamics of the predator-prey system on evolving domains is studied,and corresponding models of the predator-prey system are established in the growing domain and the periodically evolving domain respectively.The predator and prey population behaviors are analyzed with the help of principal eigenvalues,and the important impacts of two types domain evolution on the survival of predator and prey populations are revealed.This paper is divided into the following five parts.In chapter 1,we mainly introduce the research background and recent research status of the problem,including the history of research on evolving domains,the current status of research about predator-prey models on evolving domains,and expound the overall arrangement of the paper.In chapter 2,we introduce the establishment of a predator prey model on evolving domains.Based on assumptions,the process of transforming from evolutionary domains to fixed domains about a predator-prey system is explained in detail,and introduce relevant basic knowledge.In chapter 3,we study the predator-prey system on the growth domain.With the help of the principal eigenvalues,we analyze the existence of steady-state solutions of the limit system by applying the comparison principle and the strong maximum principle.On this basis,we investigate the asymptotic properties of solutions by constructing upper and lower solutions and monotonic iterative sequences.And the dynamics of the system on the fixed and growth domains are compared and analyzed to illustrate the effect of the evolution of the growth domain on the survival of the population.Then,we use Matlab software to simulate the results on the two different domains,and obtain conclusions which are consistent with the theoretical results.In chapter 4,we study the predator-prey system on the periodic evolution domain,and analyze the principal eigenvalues of the periodic system.According to coupled upper and lower solutions and the comparison principle,we obtain the existence of positive periodic solutions.The dynamic behavior of a predator-prey systems on the fixed domain and the periodically evolving domain are compared and analyzed,and the impact of regional periodic evolution on population survival is described.Then,simulation verification is conducted on the predator prey system in two different domains,and it is found that it is consistent with the theoretical results.In chapter 5,we summary the main findings of this paper: larger regional evolutionary functions are beneficial for the survival of predator and prey populations,and propose a question that can be further studied.