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

In this thesis, we investigate the stability and bifurcation of two discrete Leslie-Holling systems. It consists of four chapters.Chapter one introduces the background and existing work of the growth system as well as the elementary theories which are needed in the paper.Chapter two discusses the dynamics beheviors of a discrete predator-prey model of Leslie-Holling type. we investigate the flip bifurcation and Neimark-Sacker bifurcation of the positive fixed point as well as bifurcation direction and stability by using center manifold theorem and bifurcation theory. Numerical simulation are presented not only to illustrate our results with analysis, but also to exhibit the complex dynamical behaviors such as period-7,14,16,21,22,26,31,32,42,44,47-orb-its,cascade of period-doubling bifurcation in period-2,4,8,16,32,5,10,6, 12-orbits,quasi-periodic orbits and the chaotic sets, according to Bifurca-tiondiagram, the phase diagram and the maximum Lyapunov exponent.Chapter three discusses the dynamics of a discrete predator-prey model of Leslie-Gower type. Including the existence and stability of the nonnegative fixed points, and the system undergoes flip bifurcation and Neimark-Sacker bifurcation at the positive fixed point. Numerical simulation are presented not only to illustrate our results with analysis, but also to exhibit the complex dynamical behaviors such as period-6,9, 10,12,14,16,18,20,40,59,77-orbits, cascade of period-doubling bifurcation in period-2,4,8,16,32-orbits quasi-periodic orbits and the chaotic sets, accor-ding to bifurcation diagram, the phase diagram and the maximum Lyapu-nov exponent.Chapter four, summarizes the mainly work of this paper, and carry on the results to further discusses.