Dynamic Behaviors Of Three Classes Of Stochastic Biological Population Models

Population dynamics is a science that utilizes mathematical methods and theories to study the law of biological population development.At first,scholars studied popu-lation dynamics by establishing deterministic mathematical models.Among them,the Lotka-Volterra model is the earliest mathematical model to describe the relationship between species.On this basis,a variety of ecosystem models have emerged,and the dynamics behavior of the population in these deterministic models has been studied,and abundant research results have been obtained.However,there are many uncer-tainties and random environment factors in nature,these factors are bound to affect the dynamic behavior of the population to varying degrees,it is more suitable to de-scribe the ecological evolution process of the population with the stochastic biological mathematical model.Based on the deterministic population models,we mainly study the effect of white noise on the intrinsic growth rate of the population,and establish the corresponding stochastic population models.Furthermore,by applying the It(?) formula and using the comparison theorem of differential equation and Lyapunov analysis method,we prove there exists a global positive solution of the system.Based on the above conclusions,sufficient conditions for the existence of ergodic stationary distribution and period-ic solution of the system are obtained by using the theory of stationary distribution and periodicity developed by Has'minskii.Finally,we verify our results by numerical simulations.In chapter one,we recommend research background,research significance and the research actuality about population dynamical models.Moreover,we introduce some basic definitions and preliminaries involved in the paper.In chapter two,diffusion is a common phenomenon in nature and it plays an sig-nificant role in the evolution of a population.Based on this,we studied a predator-prey dynamics in stochastic Lotka-Volterra model with diffusion.We prove there exists a global positive solution of the system.Based on this,the conditions of stationary distri-bution of the stochastic diffusion system in_+~3are given.Furthermore,the existence of periodic solution in the system is proved when all the coefficients are periodic functions.In chapter three,there are many different types of functional responses to describe the average rate of the predator consumption of the prey in the predator-prey mod-el.Thereby,we consider a stochastic two-predators one-prey system with modified Leslie-Gower and Holling II schemes.It is first pointed out that there is a stationary distribution of the stochastic system in_+~3.Furthermore,the existence of periodic solution in the system is proved when all the coefficients are periodic functions.In chapter four,considering the predator population is not only affected by the intrinsic growth rate and mortality,also will be affected by the influence of energy conversion parameter of prey into predator.Therefore,we introduce energy conversion parameter to the stochastic Lotka-Volterra model with one prey and two predators.We prove the global positivity of solution with the positive initial values.Moreover,we ob-tain the sufficient conditions which guarantee the existence of a stationary distribution and periodic solution.In chapter five,we summary our works,and indicate the shortcomings of this paper.Then,we make a prospect for the future work.