Stability analysis of the euler discretization for the harvesting Leslie-Gower predator-prey model

In this paper, a harvesting Leslie-Gower equations is discretized using the forward Euler method. The dynamical properties of the resulted discrete system is then analysed. It is shown that the discrete system has exactly the same equilibria as those of original continuous equation. However, the stability of positive equilibrium is dynamically consistent with its continuous version only for relatively small time step. Such behaviour is confirmed by our numerical simulations. Furthermore, our numerical simulations show when the time step does not satisfy the stability condition, the discrete system has more complicated dynamics such as period-2ⁿ-orbits and chaos.