Stability analysis and Neimark-Sacker bifurcation of a nonstandard finite difference scheme for Lotka-Volterra prey-predator model

Abstract

To discretize the Lotka-Volterra prey-predator model, we adopted a dynamically consistent nonstandard finite difference scheme. The existence of fixed points and their topological categorization are examined. It is proved using bifurcation theory that the system experiences Neimark-Sacker bifurcation. Moreover, the hybrid control method is used to control the Neimark-Sacker bifurcation. Additionally, numerical simulations are performed to show the system’s complexity and consistency with analytical results.