Nonstandard Finite Difference Theta Approaches to the Predator-Prey System

Abstract

In this paper, we propose nonstandard finite difference theta schemes for a well-known Lotka-Volterra model without the Allee effect and investigate the dynamical behavior of the discretized system. We prove that the scheme is dynamically consistent with the continuous model, preserving key properties such as the positivity of solutions and the stability of equilibrium points. Numerical experiments are conducted to validate the theoretical results and demonstrate the superiority of the proposed schemes over standard methods in maintaining these critical properties.