Analysis Of Dynamical Models Subject To Allee Effect

In this paper,we consider three kinds of species models subject to an Allee effect.This paper is divided into four chapters:In chapter 1,firstly,we introduce the study background of species models subject to an Allee effect and some important results of that former scholars have studied.Secondly,some principal definitions and theorems are cited which will be utilized in the following chapters.In chapter 2,we study a predator-prey system with Allee effect for prey.In addition,we discuss the properties of equilibrium points and the existence and uniqueness of limit cycle,in this way,the conditions of predator species extinction are obtained.In chapter 3,we consider the corresponding periodic system of the model in chapter2.Using continuation theorem in coincidence degree theory,we get the sufficient conditions for the existence of periodic solution.Finally,we discuss the global attractability of periodic solution with Lyapunov functional method.In chapter 4,we discuss the development issues of biological populations subject to an Allee effect.In the first place,we consider the capture conditions of single species with Allee effect.Next,we construct a new predator-prey system with Allee effect for prey and capture prey,study the properties of equilibrium points and the existence of limit cycle as well.