Dynamics Analysis Of Two Kinds Of Biological Population Models With Feedback Control

In this paper,we study the dynamic properties of biological population from the mathematical point of view,use mathematical tools such as stochastic differential equation to model and analyze,and discuss the influence of environmental noise and feedback control measures on biological population behavior.This paper mainly discusses two kinds of biological population models,one is a stochastic Leslie-Gower predator-prey model with feedback control,the other is a nonautonomous stochastic predator-prey model with Allee effect and feedback control.In the first chapter,we briefly introduce the knowledge of ordinary differential equation and stochastic differential equation,as well as the definition and theorem of the existence of periodic solution.In the second chapter,a stochastic Leslie-Gower predator-prey model with feedback control and Holling type II functional response is established.Firstly,it is proved that the model has a unique global positive solution;secondly,the existence condition of positive recurrence of the system is obtained by establishing a suitable Lyapunov function;in addition,the condition of population persistence and extinction is obtained by using the comparison theorem of stochastic differential equation and the law of large numbers;finally,the result is verified by numerical simulation with Matlab.In the third chapter,a kind of nonautonomous stochastic predator-prey model with Beddington-DeAngel functional response,additive Allee effect and feedback control is established.Firstly,by constructing a suitable Lyapunov function,the existence and uniqueness of the global positive solution of the system are proved.Secondly,by using the technique of formula and inequality,the condition of periodic solution is obtained.Then,we discuss the conditions of permanence or extinction of the system under white noise interference.Finally,the theoretical results are explained by numerical simulation.In the fourth chapter,we summarize the main work of this paper and put forward the next research direction.