Analysis Of Stochasticcrop Diseases And Insect Pests Model Affected By Insecticides

Population ecology is a science that originates from demographics to study the law of the development of biological populations.Its research the method mainly understands,explains and predicts the development and change law of various species in nature through mathematical models,so as to achieve the purpose of better management and protection of biological populations in ecological environment.The main research content of this paper is to establish crop,pest and insecticide models affected by white noise and Levy noise,and study the dynamic behavior of the models.The details are as follows:In Chapter 1,introducing the research background and status quo of pest control,and gives the relevant basic concepts and lemma.In Chapter 2,a model of crop pests and diseases with white noise and insecticides is presented.Firstly,the existence and uniqueness of the global positive solution of the model is proved.Secondly,sufficient conditions for the extinction and persistence of the system are obtained by using the existing theorems and relevant definitions.Then,we construct proper Lyapunov function according to the characteristics of the system equation,and prove the existence of stationary distribution by using the ergodic theory given by Khasminskii.We use exponential martingale inequality and Borel-Cantelli lemma to estimate the asymptotic path of system solutions.Finally,Matlab is used to verify the numerical simulation results.In Chapter 3,we consider the influence of Levy noise on the basis of Chapter 2.Firstly,the existence and uniqueness of the global positive solution of the model is proved.On this basis,the sufficient conditions of extinction and permanence of the model are studied and the asymptotic path is estimated.Finally,the main research results of this paper are summarized and the prospect is put forward.