Best" nonlocal discretization method for 2-dimensional population models

I will present a nonstandard finite difference method designed for numerical simulation of 2-dimensional mathematical models of population dynamics. The proposed method is based solely on the principle of nonlocal discretization. Independently of the chosen step-size of simulation, both the original population model and the discrete model derived by our method exhibit the same qualitative behaviour around asymptotically stable equilibrium points. The non-negativity of the solution and instability of equilibrium points is preserved as well. What is more, our preliminary simulations reveal that this method may also preserve stable limit cycles