Bifurcations And Stability Of A Biological Economic System With Allee

The paper analyzes the stability and Hopf bifurcation of a bioeconomic system with Allee through the differential-algebraic system theory, and numerical imulations are performed by MATLAB to illustrate the analytical results.Then, a discrete system is obatained by appyling the Euler scheme to the system.Flip bifurcation and Neimark-Sacker bifurcation is studied by choosing step as bifurcation parameter. This paper is divided into five chapters.The first chapter intoduces the background of this paper, the modelling process of the differential-algebraic system and the practice meanings, the main results and innovation is also pointed.The second chapter shows prearrangent knowledge and intoduces the theory of differential-algebraic system, Hopf bifurcation, Flip bifurcation and Neimark-Sacker bifurcation.In the third chapter, a bioeconomic system with Allee is considered by using the differential-algebraic system theory and Hopf bifurcation theory.In the fourth chapter, applying the Euler scheme to original system, then a discrete system is gained.By selecting step as bifurcation parameter, we discussed Flip bifurcation and Neimark-Sacker.Numerical simulations are given to illustrate the analytical results.The last chapter is a summary and an outllook of this thesis.