Multiple Bifurcations In A Predator-prey System With Non-monotonic Functional Response And Constants Harvesting

Bifurcation theory is widely used in disease prevention and biological system which has caused scientist’s more and more attention. Specially, bifurcations in a biological model with nonmonotonic functional response and harvesting, it can lead the human to explore resource reasonably, and has a good effect on protect ecosystem.In this thesis, we will study the dynamical properties of a Predator-Prey system with non-monotonic functional response and constants harvesting. First we intro-duce the researching status and sense about the bifurcation of the Predator-Prey system. Then we discuss the existence of the equilibria and stability, and various types of dynamical behavior in the small neighborhood of the equilibrium for the model (2.1), by theory of stability. At last in section3, we study bifurcations of model (2.1) depending on vary parameters, by bifurcation theory. We show that the model exhibits the Hopf bifurcation of codimension1and2, the cusp bifurcation of codimension2, and the cusp of codimension3. Hence, there are different parameter values for which the model has a limit cycle, or a homoclinic loop, or two limit cycles, or the coexistence of a limit cycle and a homoclinic loop.