Two Types Of Discrete Leslie Predator Prey System Stability And Bifurcation Analysis

In this thesis, the dynamics of two discrete-time predator-prey systems of Leslie type are investigated in the closed first quadrant. It consists of three chapters.In the first chapter, the background, the recent works of the predator-prey system and the preliminaries are introduced.In the second chapter, the complex dynamics of the predator-prey system of Leslie type with Beddington-DeAngelis functional response are discussed, including the existence and the stability of positive fixed point. By using bifurcation theory, we show that the system undergoes the Flip bifurcation and Neimark-Sacker bifurcation when the parameters vary. Numerical simulations are presented to exhibit cascade period-doubling bifurcation, such as the period-2,4,8,16 orbits, invariant circle, periodic windows in Neimark-Sacker bifurcation, quasi-periodic orbits and the chaotic sets. At last we have stabilized the chaotic orbits to an unstable fixed point via the feedback control method.In the third chapter, the complex dynamics of the predator-prey system of of Leslie type with general Holling functional response are studied, including the existence and the stability of positive fixed point, the Flip bifurcation and Neimark-Sacker bifurcation at the positive fixed point via bifurcation theory, controlling chaos by using the feedback control method. Numerical simulations are presented to confirm the theoretical analysis. Also the bifurcation diagrams, phase portraits and Maximum Lyapunov exponents are computed to confirm the complexity of the dynamical behaviors.