Study On The Dynamic Properties Of A Stochastic Predator-Prey Model

Population ecology is a science that originates from demographics to study the laws of the development of biological populations.The research method is to understand,explain and predict the relevant changes in the development laws of various biological species in nature through mathematical models,it aims to manage and protect biological populations in the ecological environment.The contents and research methods of the paper are as follows:First,the research background,research status and research progress of the predator-prey model of Holling ? type functional response are introduced,and then some basic definitions,theorems and lemmas used in the paper are introduced.Then mainly considers the classic predator-prey model with Holling ? type functional response under regime switching and white noise interference.Using the ergodic property of the one-dimensional system(3.1)and constructing an appropriate Lyapunov function,as well as establish sufficient conditions for the strong persistence in the mean and the extinction of the predator population in system(1.3),and obtain the threshold between them.By applying the ergodic property given by Khasminskii and the Lyapunov function method,conditions that to ensure the stochastic model has a unique ergodic stationary distribution can be obtained.In Notes 3.1 and 3.4,This paper estimate upper and lower bounds of ? to determine the specific effects of large and small white noise on system persistence and extinction.It can also be found that the presence of the Markov chain in this stochastic system can contribute to the survival of the population,and reduce the risk of extinction,which can be seen from the example and figures.The fourth chapter summarizes the main research results of this paper and proposes future research directions.