# Nonstandard finite difference schemes for a general predator-prey system

## TL;DR

This paper develops a nonstandard finite difference scheme for predator-prey models, ensuring dynamic consistency and stability, with numerical simulations validating the theoretical findings.

## Contribution

It introduces a novel NSFD scheme for predator-prey systems that preserves stability and dynamics across any step size, including non-hyperbolic equilibria.

## Key findings

- NSFD scheme maintains dynamic consistency with continuous models
- Global stability of non-hyperbolic equilibrium proved
- Numerical simulations confirm theoretical stability results

## Abstract

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.