Dynamic Behavior Of Some Stochastic Population Models

Stochastic diferential equation was a cross discipline which developed around the middleof the20th century, has been widely applied in life science, economics and finance, controltheory, aerospace engineering, etc., Such a broad range of applications made the study ofstochastic diferential equations particularly important.This paper mainly analysis and studies the dynamics behavior of several types of thepopulation dynamics stochastic models, the main content is divided into three parts:Firstly, We consider a classic population dynamic model with impulsive toxicant inputand environmental noise efect on the population, the predator-prey model with impulsiveefect and random disturbance are studied, in order to obtain the dynamic behaviors of suchsystem better.Secondly, We established two species stochastic model with Gompertz functional re-sponse, the population models of Gompertz growth merge environmental noise, we obtainsome complex and interesting dynamical behaviorsThirdly, We consider two-species stochastic population model with impulsive and Holling-type IV functional response. Using the comparison theorem of stochastic diferential equationand formula to study the dynamic behavior of the model.