Dynamic analysis of a predator-prey model with Holling type-II functional response and prey refuge by using a NSFD scheme

Abstract

This study proposes and analyzes a nonstandard finite difference (NSFD) scheme to retain the fundamental qualitative aspects of a predator-prey interaction with a Holling type-II functional response and prey refuge. The existence and stability of fixed points are examined. A few numerical examples are presented to back up the theoretical findings. The results show that the numerical simulations match well with the theoretical outcomes. Moreover, the model experiences transcritical, period-doubling, and Neimark-Sacker bifurcation. Furthermore, numerical simulations show that standard numerical methods like the Euler method and the classical RK4 method are not dynamically consistent with the continuous model. As a result, they do not accurately reflect the continuous model’s behavior. The proposed NSFD scheme, on the other hand, is shown to be suitable and adequate for solving the continuous model.