Dynamic Analysis Of Stochastic Population System

Population model is an important mathematical model in biological mathematics,which extensively describes some problems in many fields,such as population model,food chain model in ecosystem,and saving endangered species model,etc..However,when these problems are mathematically modeled,their processes are inevitably subject to the stochastic external disturbances.At this time,when considering the external stochastic interference,the model is the stochastic population model.As we know,the number of a population at some time not only depends on the current state of the population,but also the state of the population over the past period of time.In addition,It shows from the theoretical analysis that time delay can change and affect the performance of the system.On the other hand,compared with the stochastic differential equation driven by Brownian motion,the stochastic differential equation driven by Lévy noise can better describe some realistic problems in many fields,such as finance engineering,network engineering,system engineering and population ecology,etc.Therefore,this paper mainly focuses on the dynamic behavior of stochastic delay population model driven by Lévy noise.This Master's degree thesis is divided into four chapters:In the first Chapter,we mainly introduce the development of stochastic delay population model driven by Lévy noise,the research achievements at home and abroad,some preliminary knowledge and the common notations used in this paper.In the second Chapter,the Lyapunov functional method is used to consider the existence of globally positive solutions,stochastic ultimate boundedness and the asymptotic pathwise properties of stochastic population model with distributed delay driven by Lévy noise.In the third Chapter,the Lyapunov functional method is employed to analyze the existence of globally positive solution,and the asymptotic stability in distribution for stochastic delay population model driven by Markov chain and Lévy noise.In the fourth Chapter,the summary and the prospect are made.