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 is shown that the system can undergo fold bifurcation, flip bifurcation, and Neimark-Sacker bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations are presented to illustrate the main theoretical results. Compared to the continuous analog, the discrete system here possesses much richer dynamical behaviors including orbits of period-16, 21, 35, 49, 54, invariant cycles, cascades of period-doubling bifurcation in orbits of period-2, 4, 8, and chaotic sets.

Keywords

• discrete predator-prey system
• leslie-gower
• michaelis-menten type harvesting
• fold bifurcation
• flip bifurcation
• neimark-sacker bifurcation
• 34c25
• 92d25
• 34d20
• 34d40