Transcritical and Neimark-Sacker bifurcations of a discrete predator-prey model of γ-Ricker type with double Allee effect in the prey population

This article focuses on investigating the dynamics and bifurcations of a new discrete-time predator-prey model of the γ -Ricker type with a double Allee effect in the prey population. Using a γ -Ricker growth model to define the prey population enables an analytical approach to be taken to the subject, involving the use of Lambert W functions to explicitly determine the predator-free fixed points. Applying this type of transcendental functions allows that fold bifurcations to be identified and an original complex bifurcation structure to be created, which combines the intervention of two distinct predator-free fixed points and also of the origin. This new type of bifurcation for discrete-time predator-prey models could lead to the extinction of the populations involved in the system, and is called a double Allee bifurcation. Other types of bifurcation are recognized, including flip, transcritical and Neimark-Sacker bifurcations, as well as local bifurcations of codimension two or greater, including their ecological interpretations.