Study On Delays And Noises In Two Models With Saturation Effect

In this thesis,by using the theory of delay differential equations,impulsive differential equations and stochastic differential equations,the dynamical behaviors of two stochastic population models with saturation effect are studied with the help of constructing appropriate Lyapunov functions and some inequality techniques.The main contents are as follows.The first chapter briefly introduces the ecological backgrounds,significances,status and the main works of this paper.The second chapter mainly gives the relevant symbol descriptions,definitions,lemmas and important inequalities.In the third chapter,based on a competitive model with saturation effect and distributed delay and considering two coupling noise sources,a corresponding stochastic competition model is established.By constructing appropriate Lyapunov functions,some properties of this stochastic competitive model are discussed and sufficient conditions of exponential extinction,extinction,persistence in the mean,existence and uniqueness of stationary distribution are gained.Furthermore,numerical simulations are carried out to verify our theoretical results.In the fourth chapter,based on a mutualism model with saturation effect and impulsive toxicant input in a polluted environment and considering stochastic perturbations modeled by a mean-reverting Ornstein-Uhlenbeck process,a corresponding stochastic mutualism model is established.By constructing appropriate Lyapunov functions and using It(?)'s formula and some inequality techniques,some properties of the solution of this model are studied,including exponential extinction,persistence in the mean,stochastic permanence and other dynamic properties.At last,numerical simulations are shown to verify our theoretical results.