Stablity And Bifurcation Analysis Of Two Discrete Amensalism Models

The interaction between species has always been the core problem of ecology and biology.The amensalism model is one of the important models,and its mathematical research has strong biological significance.Allee effect is an important phenomenon in population dynamics.It is found that Allee effect has a very important impact on biological systems,and shows complex dynamic characteristics.This paper studies the dynamic behavior of two kinds of discrete amensalism models with weak Allee effect,the existence,the stability and the bifurcations are analyzed.For non -hyperbolic fixed points,the stability is discussed by using the central manifold theorem,and the trend of solu-tion sequence near them is analyzed.The fold bifurcation and flip bifurcation are analyzed by using theory of the restricted normal form.Finally,we provide numerical simulations to demonstrate our theoretical results.The results show that the discrete system has more complex dynamic behaviors than the con-tinuous system,and the step size has an effect on the stability of the fixed point.When the step size is selected as the control parameter,the system will undergo flip bifurcation.The paper is divided into five chapters.The first chapter introduces the research background and significance,the results obtained in the literature and the main work of this paper? The basic knowledge and theorems used in this paper are provided in the second chapter? The third chapter studies a kind of discrete amensalism model with Allee effect for the first species,the existence,stability and bifurcation of all possible boundary fixed points and coexistence fixed points are discussed? In the fourth chapter,the dynamics on a kind of discrete amensalism model with Allee effect for the second species are given,which including the existence,stability,bifurcation of all possible fixed points,and the numerical simulation are provided to illustrate the results? The fifth chapter summarizes the work of this paper and shows the further research plan.