Bifurcation and chaos in a discrete predator-prey system of Leslie type with Michaelis-Menten prey harvesting

Abstract In this paper, a discrete Leslie-Gower predator-prey system with Michaelis-Menten type harvesting is studied. Conditions on the existence and stability of fixed points are obtained. It shown that can undergo fold bifurcation, flip Neimark-Sacker bifurcation by using center manifold theorem theory. Numerical simulations presented to illustrate main theoretical results. Compared continuous analog, here possesses much richer dynamical behaviors including orbits period-16, 21, 35, 49, 54, invariant cycles, cascades period-doubling in period-2, 4, 8, chaotic sets.