Stability preserving non-standard finite difference scheme for a harvesting Leslie–Gower predator–prey model

Abstract

A non-standard finite difference scheme for a harvesting Leslie–Gower equations is constructed. It is shown that the obtained difference system has the same dynamics as the original continuous system, such as positivity of solutions, equilibria and their local stability properties, irrespective of the size of numerical time step. To illustrate the analytical results, we present some numerical simulations.

Keywords::

• predator–prey model
• difference equation
• unconditionally positive
• dynamically consistent
• asymptotically stable
• discrete Leslie–Gower equation

AMS Subject Classification::

• 03H05
• 37N25
• 37N40
• 92D40

Disclosure statement

No potential conflict of interest was reported by the authors.