Qualitative Analysis Of Two Biological Models With Cannibalism

In recent years,the bifurcation theory of differential equations has been widely used in various fields,especially in biological mathematics.In this paper,two kinds of predator-prey models with cannibalism are selected as research objects.The main research contents are as follows:Chapter 1 mainly describes the background,significance and research status at home and abroad.In Chapter 2,the relevant theoretical knowledge of dynamical systems and bifurcation theory is briefly introduced.In Chapter 3,the parameters of a given continuous predator-prey model with predator cannibalism are simplified,and its discrete version is obtained by using the semidiscretization method.Then the existence and stability of the fixed points of the discrete system are investigated.The bifurcation at the fixed points is obtained by using the central manifold theorem and the local bifurcation theory.The conditions for the occurrence of transcritical bifurcation of the discrete system are proved.In Chapter 4,a discrete predator-prey model with Allee effect and cannibalism is studied by using similar methods to the last chapter.The stability of its fixed points is completely analyzed,and the sufficient conditions for the occurrence of period-doubling bifurcation and Neimark-Sacker bifurcation at the positive fixed point of the system are obtained.The bifurcation diagram,Lyapumov exponent diagram and phase diagrams are given by numerical simulations,which verify the previous conclusions.Chapter 5 summarizes the content of the full paper,and puts forward some prospects for further research.