  In this paper we transform a continuous-time predator-prey system with
general functional response and recruitment for both species into a
discrete-time model by nonstandard finite difference scheme (NSFD). The NSFD
model shows complete dynamic consistency with its continuous counterpart for
any step size. Especially, the global stability of a non-hyperbolic equilibrium
point in a particular case of parameters is proved by the Lyapunov stability
theorem. The performed numerical simulations confirmed the validity of the
obtained theoretical results.
