Bifurcation And Control For Two Type Leslie-gower Predator-prey Differential Algebraic System With Nonlinear Harvesting

In this paper, using stability theory and bifurcation theory, and combined with differential algebraic systems, the stability of the positive equilibrium of the two types of Leslie-Gower predator-prey differential algebraic system with nonlinear harvest has been investigated, then the dynamic characteristics and bifurcations have also been studied for the two types system at which the ecological economic profit is zero or positive. At last, this paper also gives the control for the system’s bifurcation when the ecological economic profit is zero or positive.The first part, it gives a summary overview for the current status of ecological mathematics’ research, then it focuses on the real sense of the Leslie-Gower predator-prey differential algebraic system with nonlinear harvest.The second part, when economic profit is zero, the study discusses the first class Leslie-Gower predator-prey differential algebraic system with nonlinear harvest.The system’s stability and SIB has been studied, and it gives control for SIB.The third part, based on a more realistic sense of the second class Leslie-Gower predator-prey differential algebraic system with nonlinear harvest, here it has researched the stability of the positive equilibrium state of the system, and the Hopf bifurcation of the system, and the washout filter control method is used to control the Hopf bifurcation.