The Long Time Behavior Of Stochastic Single Population Biological Growth Models With Markov Switching

Many scholars set up deterministic models to study the dynamic behavior of biological models.However,any biological individual in nature is inevitably influenced by the random factors such as the change of its own quantity and the external environment.Therefore,the stochastic models can reflect the actual situation more accurately.In this paper,we use stochastic differential equations and Markov process theory to study the long time behavior of stochastic single species population growth models with Markov switching.This article is divided into five chapters,the main contents are as follows:In the first chapter,we introduce the background and significance of the models,and then summarize the main contents and innovations of this paper.In the second chapter,this chapter first gives the preliminary knowledge of this paper,then a stochastic single population biological growth model with Markov switching is constructed by introducing white noise and Markov chain into a deterministic single population biological growth model,and studies the global existence of the positive solution of the model.In the third chapter,applied generalized I to formulas,ergodic theory of Markov processes and stochastic analysis techniques,we study the stochastic persistence and extinction of the stochastic population growth models with Markov switching,and asymptotic property etc.The algebraic rules are given to be easy to judge.In the fourth chapter,numerical examples are given and numerical simulations are carried out.The fifth chapter is a summary of the contents of this paper.