Population Dynamical Models On Periodically Evolving Domain

This paper studies the dynamical behavior of populations subject to the periodically evolving domain,the main works focus on the impacts of the periodically evolution of the domain,where periodically evolving domains are the domains changed periodically with time.First,this paper studies the Logistic model on the periodically evolving domain.With the help of eigenvalue theory,the effect of the periodically evolution of the domain and the evolving frequency of the domain on the population dynamics is analyzed,and the theoretical results obtained are verified by numerical simulation.Secondly,this paper also studies two populations of Lotka-Volterra competitive systems and predator-prey systems with Dirichlet boundary conditions on the periodically evolving domain,and analyzes the effects of the periodically evolution of the domain and the population diffusion rate on the dynamic behavior of the two-population systems.This effect is related to the integral value of the reciprocal of the evolution function within a period.In general,large evolution is conducive to coexistence of populations,and small evolution is not conducive to coexistence of populations;and for a certain periodically evolving domain,small diffusion rate is conducive to coexistence of populations,and large diffusion rate is not conducive to coexistence of populations.