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 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.