Analysis Of Several Types Of Random Population Models

Population ecology depicts the law of interaction between population dynamics and the objective environment,which plays an important role in basic and applied ecology.It is worth noting that the real world is full of uncertainties and random factors,especially,noise can affect the dynamic changes of population and make the population produce random oscillation.Therefore,it has practical significance and theory value to study the stochastic population model with noise.In this paper,we mainly study three types of stochastic population model:stochastic intraguild predation with L?evy noises,stochastic food chains models in a polluted environments,and stochastic apparent competition with a protection zone.The second chapter mainly investigates dynamic properties of stochastic intraguild predation with L?evy noises.The intraguild predation describes the phenomenon that a predator feeds on another predator while competing for the common resource.In this chapter,the stochastic persistence and extinction of a population under random perturbation is established,and the asymptotic stability of the solution of the model in the sense of distribution is given.In the third chapter,the dynamic properties of a stochastic food chains model in a polluted environments are discussed.As a result of the relationship of environmental pollution,the toxin in the natural environment increases gradually and threatens the survival of the population.This chapter explores the sufficient conditions for the population to be extinct,stochastic non-persistence,stochastic weak persistence,stochastic strong persistence,and stochastic persistence for the food chain model under the combined action of toxin and noise,and the existence and ergodicity of the stationary distribution of the model.In the fourth chapter,the dynamic properties of stochastic apparent competition with a protection zone are studied.Apparent competition describes the phenomenon of indirect competition between two prey species through a common predator.It is of great significance in biological invasion and protection of biological diversity.In this chapter,the stochastic persistence and extinction of the population in apparent competition are established in a protection zone.