Weak Persistence Of Stochastic Delayed Competition System With Allee Effect And Noise Disturbance

In recent years,the study of dynamic system of competitive population has attracted the attention of many scholars.With the rapid development of social industrialization,the ecological environment is increasingly damaged,so need to investigate the related properties of competitive population dynamics in order to achieve sustainable development of the ecosystem.This thesis is divided into three sections.Firstly,the significance of this study,the related concepts in the population,the’development process of the population model with Allee effect,and the development process of the population model with noise disturbance as well as some related research results are introduced.Secondly,stochastic systems with Holling-Ⅱ and Holling-Ⅲ functional response functions are considered respectively,both of which are stochastic time-delay competitive systems with Allee effect and noise disturbance.Then,the existence and uniqueness of the global positive solutions and the stochastic ultimate boundedness of the solutions of the two systems are discussed.To further study the weak persistence of the two competitive systems,sufficient conditions for weak persistence are obtained by constructing appropriate stochastic Lyapunov functions and using It(?)’s formula.Finally,make a summary and outlook,put forward some shortcomings.