Chaos control & bifurcation analysis of a non-standard finite difference scheme for harvesting effects on a discrete Leslie-Gower type model

A discrete-time prey-predator system of Leslie-Gower type with harvesting is considered in this paper. The system is first discretized using the Forward-Euler method. The topology and stability of the fixed points of this method are discussed using period-doubling and Neimark-Sacker bifurcation analysis. Secondly, a non-standard finite difference scheme of the same system is presented. We have shown the permanence and dynamical consistency of this scheme. It has been shown that our non-standard finite difference scheme is the best scheme for this system, according to Mickens. Using the center manifold theorem, the normal form of the Neimark-Sacker bifurcation has been derived. Numerical simulations are provided, using a computer package, to illustrate the consistency of the theoretical results. Finally, chaos control techniques have been applied to control the chaotic dynamics of the system.