Dynamic Stability And Bifurcation Of Two Typical Biology Systems With Harvesting

Critical depensation mode and predator-prey mode of Holling II function response are two typical modes in biology mathematics. It is important to research dynamic stability and bifurcation for us to exploit and reserve natural resource.This thesis discusses dynamic stability and bifurcation of critical depensation mode and predator-prey mode of Holling II function response with qualitative theory of differential equation and modern control theory.There are four chapters in this thesis. In the second and third chapters, we discuss optimal exploitation mode of critical depensation system under constant harvesting and linear harvesting, analyze distribution and stability of equilibrium points, find the points of bifurcation of equilibrium points, and verdict the existence of Hopf bifurcation.In the forth and fifth chapters, we discuss dynamic character of a kind of predator-prey system which has Holling II function response under constant harvesting and linear harvesting of prey. These two chapters all investigate the behavior of equilibrium points, the condition of existence of limit cycle and the points of bifurcation of equilibrium points. Finally, Lyapunov approach is used to discuss the phenomenon of Hopf bifurcation. At the same time, the ecological meanings are interpreted, and simulative pictures of limit cycles are drawn.