Discrete-time bifurcation behavior of a prey-predator system with generalized predator

In the present study, keeping in view of Leslie-Gower prey-predator model, the stability and bifurcation analysis of discrete-time prey-predator system with generalized predator (i.e., predator partially dependent on prey) is examined. Global stability of the system at the fixed points has been discussed. The specific conditions for existence of flip bifurcation and Neimark-Sacker bifurcation in the interior of R+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$R^{2}_{+}$\end{document} have been derived by using center manifold theorem and bifurcation theory. Numerical simulation results show consistency with theoretical analysis. In the case of a flip bifurcation, numerical simulations display orbits of period 2, 4, 8 and chaotic sets; whereas in the case of a Neimark-Sacker bifurcation, a smooth invariant circle bifurcates from the fixed point and stable period 16, 26 windows appear within the chaotic area. The complexity of the dynamical behavior is confirmed by a computation of the Lyapunov exponents.