Research On The Bifurcation Problem Of Two Discrete Systems

The bifurcation theory of differential equations not only has an important position in the field of applied mathematics,but also has many applications in other disciplines and in life.Therefore,the study of bifurcation problems has both theoretical and practical significance.Bifurcation can exist in both discrete and continuous systems.In this paper,we mainly study the bifurcation problems of several classes of discrete systems.In this paper,the existence and stability of the fixed point of the epidemic discrete model are analyzed,and the parameter conditions for the occurrence of transcritical bifurcation,period-doubling bifurcation and Neimark-Sacker bifurcation are obtained by using the central manifold theorem and the local bifurcation theory.Finally,MATLAB is used to carry out numerical simulation,and the corresponding bifurcation diagram and phase diagram are given,which not only verifies the correctness of the theoretical analysis,but also shows rich and interesting dynamic phenomena.For the blowfly discrete model,the existence and stability of the fixed point of the model are analyzed,and then the parameter conditions for the occurrence of the Neimark-Sacker bifurcation are obtained by using the central manifold theorem and the bifurcation theory.Finally,the corresponding bifurcation diagram and phase diagram are given by numerical simulation with MATLAB,and the correctness of the theoretical results is verified.