Dynamic Behavior Of Two Classes Of Stochastic Predator-Prey Models

Population ecology is a science which research the development law of the biological population.Its research methods is using differential equations to predict the change of each species.But in the real world,population systems are always subject to random disturbances of various forms.Therefore,using stochastic differential equation to study population model can better describe the law of population development,which is more conducive to reveal the quantity change of each population in ecological society,and provide theoretical basis for the development and protection of ecological resources.In this paper,we use Lyapunov analysis method and Has’ minskii stationary distribution theory to study two kinds of random predator-prey models under white noise.we study the existence and uniqueness of the positive solutions of the above two types of models in this paper.Secondly,the sufficient condition for the existence of stationary distribution is given.Finally,the non-persistence of the model is studied.It is divided into the following two parts:In the first part,we study the random predator-prey model with Smith growth and Holling II type.Firstly,we use Lyapunov analysis method to study the existence and uniqueness of the model solution,and the solution is a global positive solution.In addition,by using Has ’minskii theory we obtain the sufficient condition for the existence of stationary distribution.Furthermore,when the noise intensity is high enough,all the populations will die out.In the second part,we study the random predator-prey model with selective capture and self-limiting predator,and study the existence,uniqueness and non-persistence of the positive solution of the model.Using the stationary distribution theory of Has’ minskii we obtain that the model has stationary distribution and ergodic property.