Bifurcation Analysis of a Discrete Predator-Prey Model with Gompertz Growth and Increased Functional Response

Abstract

This study examines a discrete predator-prey model that employs a Gompertz growth function for the prey and a Holling type I functional response. Initially, the research explores the existence and local stability of fixed points within the system, employing a fundamental lemma. Subsequently, the conditions necessary for the emergence of transcritical and Neimark-Sacker bifurcations of the system are established through the application of the center manifold theorem and bifurcation theory. Finally, numerical simulations are performed to confirm the existence of the Neimark-Sacker bifurcation.