Qualitative behavior of a two-dimensional discrete-time prey–predator model

Abstract

In this article, we discuss the qualitative behavior of a two-dimensional discrete-time prey–predator model. This system is the result of the application of a nonstandard difference scheme to a system of differential equations for a prey–predator model including intraspecific competition of prey population. In particular, we evaluate the fixed points of the system and study their local asymptotic stability. We also prove the existence of a Neimark–Sacker bifurcation.