Dynamic Behavior Analysis Of Several Types Of Predator-prey Models

As we all know,in order to fully understand and characterize the processes of the generation,coexistence and extinction of different populations,as well as the interaction between different populations,many predator-prey models are established and people investigate the complex dynamics by using dynamical system approach,and then explain the underlying mechanisms of various biological phenomena.The behavior of anti-predator,Allee effect,cooperative hunting behavior and other phenomena are common in the process of population development,and these phenomena have non-negligible impacts on the growth or disappearance of biological populations,which deserve our further attention.In this thesis,we mainly consider the effects of Allee effect,anti-predator behavior,cooperative hunting behavior and other factors on the dynamic behavior of predator-prey model.This thesis is divided into four chapters.The first chapter is an introduction,which mainly expounds the research background of predator-prey model,as well as the latest progress of current research at home and abroad,then introduces the main research content of this thesis and the process of model establishment.Finally,the basic formulas and theorems used in this thesis are also given.In the second chapter,we use the theory of dynamical system bifurcation to study the complex dynamical behavior of a predator-prey model with Allee effect,anti-predator behavior and Holling Ⅳ type functional response.The influence of anti-predator term,the existence and stability of its equilibrium point are analyzed,and the cusp point of codimension 3,the saddle-node bifurcation,the Bogdanov-Takens bifurcation of codimension 2 and 3,the Hopf bifurcation of codimension 3,the limit cycle cusp of codimension 2 and other bifurcating situations are studied,and finally the complete bifurcation diagram and phase diagram are obtained by numerical simulation.The corresponding biological interpretation of theoretical results are also given.In Chapter 3,we also use the theory of dynamical system bifurcation to study the dynamic behavior of a predator-prey model with cooperative hunting and Holling Ⅲ type functional response.At the same time,the influence of anti-predator term is fully studied,the existence and stability of its equilibrium point,saddle-node bifurcation,cusp point of codimension 2,and Hopf bifurcation of codimension 3 are found,and numerical simulations are carried out to verify the theoretical results and their biological significance.We summarize our research in Chapter 4,and propose some possible future research direction.