Stability And Bifurcation Analysis Of Continuous And Discrete Predator-prey Biological Economic System With Nonlinear Harvesting

This article is based on the classic Lotka-Volterra model, with the nonlinear harvesting for the predator and using the economic equilibrium conditions to construct a differential algebraic system. First, we study the stability and Hopf bifurcation of a predator-prey with time delay and nonlinear harvesting biological economic system by using the differential algebraic system theory. Then, we get a difference-algebraic system by applying the Poincaréscheme. We discuss the stability of positive fixed point, Flip and Neimark-Sacker bifurcation by using the stability theory, the normal form of the discrete ecosystem and the center manifold theorem. Finally, the complex dynamic behaviors of the system are presented by MATLAB. The paper is composed of four chapters.The first chapter the research background of this field is introduced, the related prearrangement and theoretical knowledge. The main work and innovation of this paper are also pointed out.The second chapter choose delay ? as bifurcation parameter, we analyze the local stability and Hopf bifurcation conditions based on the differential algebraic system theory,and numerical simulation is showed by MATLAB.The third chapter a difference-algebraic system is obtained by applying the Poincaréscheme, and choose step ? as bifurcation parameter,we discuss the the stability of positive fixed point, Flip and Neimark-Sacker bifurcation by using the stability theory, the normal form of the discrete ecosystem and the center manifold theorem, and numerical simulation is showed by MATLAB.The fourth chapter a brief summary is provide, and some problems are put forward which need to be studied in the future research work.Keywords: Differential algebraic system; Nonlinear harvesting; Delay; Hopf bifurcation; Flip...