| Population ecology is a subject that describes the interaction between a population and living environment.Biologists and mathematicians use mathematical models to describe the complex interaction relationship and use them to describe and predict the development process of biological population.Considering that the population must be affected by its living environment,it is necessary and reasonable to establish the corresponding stochastic population dynamics model to model the effect of environmental noise.Combining with the relevant theoretical knowledge of biodynamic model and stochastic differential equation,the dynamic behavior of two types of stochastic population models is studied in this thesis,and some specific examples and corresponding numerical simulations are given to verify our results.This thesis is divided into four chapters as follows:The first chapter summarizes the research backgrounds,significances and status at home and abroad.Meanwhile,the major works of this thesis are stated.The second chapter provides some preparatory work.Some symbol descriptions concerned in this thesis and related definitions,lemmas and important inequalities are introduced.In the third chapter,stochastic predator-prey model with modified Leslie-GowerHolling II functional response and Ornstein-Uhlenbeck process is studied.By constructing suitable Lyapunov functional and using stochastic comparison theorem and It?'s formula,the existence and uniqueness of global positive solution and sufficient conditions for persistence in the mean and extinction are derived.In the fourth chapter,a type of stochastic mussel-algae models is established.By constructing suitable Lyapunov functional,stochastic comparison theorem and It?'s formula,we mainly focus on studying the dynamic properties of the model,including the existence and uniqueness of global positive solution,extinction,nonpersistent in the mean and weak persistence,ergodic stationary distribution and periodic solution. |
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