The Research For A Biological Economic Model Based On Differential-algebraic System

The paper mainly studies the stability and Hopf bifurcation of a biological economicmodel based on differential-algebraic system and consists of four chapters. simple explaina-tion as followsThe first chapter as an introduction。it introduce the history process of researchingthe differential-algebraic biological economic system, its important meaning, the currentresearch status and the correlative theorems quoted, the research work in this paperIn the second chapter, it mainly discuss the stability and Hopf bifurcation of adifferential-algebraic biological economic system with selective harvesting. Using a param-eterization approach of the differential algebraic system and bifurcation theory, we obtain theinterrelated stability criterion and the related conditions of producing Hopf branch of the dif-ferential-algebraic biological economic system by considering the time delay as bifurcationparameter.In the third chapter, Stability and Hopf bifurcation for a differential-algebraic biologicaleconomic system with non-selective harvesting is considered, Using a normal form approachof the differential algebraic system and Hopf bifurcation theory, we discuss all kinds of casesof stability when economic profit parameter μ means different number.Finally, the conclusion and hope are showed in the fourth chapter, and present the futuretendency and direction of research for the task.