The Stability Analysis And Singular Induced Bifurcation Of A Class Of Differential-algebraic Biological Economic System

The paper mainly studies the stability of a class of differential-algebraic biological eco-nomic system and consists of four chapters.The first chapter as an introduction, modeling process of the differential-algebraic bio-logical economic system, its real meaning, the current research status and the main work ofthis paper are addressed.In the second chapter, the stability of this kind selective harvesting differential-algebraicbiological economic system is given by using the stability of the differential-algebraic sys-tem, the conditions for the stability of the positive equilibrium point are obtained, when thepositive equilibrium point is center of the linear system, for the nonlinear system, we usecriterion successor function and discriminant formal series to discuss the center-focus of thepositive equilibrium point.In the third chapter, the stability of this kind non-selective harvesting differential-algebraic biological economic system with economic profit m = 0 is given, the switch of thestability of the positive equilibrium point is obtained, and the feedback control to remove thesingular bifurcation is designed.Finally, the conclusion is showed in the fourth chapter, and some problems we needstudy later are given.