Dynamical Analysis Of A Discrete-time Parasite-host Model

In this thesis, the dynamic characteristics of a simple discrete parasite host model are discussed as the following three chapters.In the first chapter, the significance of this topic, the research background and the current situation are introduced.In the second chapter, the necessary knowledge of discussing the dynamic properties is introduced, including the bifurcation theory related to the model, the center manifold theorem and introduce the main work of this paper.In the third chapter, applying the forward Euler discrete scheme to continuous parasite-host model, we study the dynamical properties of discrete parasite-host model.The existence and the stability of fixed point are considered, we obtain the conditions for the existence of Flip bifurcation and Neimark-Sacker bifurcation by using center manifold theorem and bifurcation theory. Then, we prove there are Marotto's chaos according to the defition of Marotto's chaos. Numerical simulations demonstrate analytical results, richer and more complex dynamical behaviors (cascade period-doubling bifurcation, such as the period-1, 2, 4, 8 orbits, invariant circle, periodic windows in Neimark-Sacker bifurcation,quasi-periodic orbits and chaotic sets). Finally, we used the feedback control method to control the chaotic orbits to an unstable fixed point. Moreover, we get a new model by replacing the mass action incidence function ?xy with a standard incidence function ?xy/x+y and obtain the improved model conditions for the existence of the Flip bifurcation and Neimark-Sacker bifurcation and discuss the biological meaning of the model.