Bifurcation Structures of the Homographic γ-Ricker Maps and Their Cusp Points Organization

Abstract

This paper aims to study the bifurcation structures of the homographic [Formula: see text]-Ricker maps in a four-dimensional parameter space. The generalized Lambert [Formula: see text] functions are used to establish upper bounds for the number of fixed points of these population growth models. The variation of the number of fixed points and the cusp points organization is stipulated. This study also observes a vital characteristic on the Allee effect phenomenon in a class of bimodal Allee’s maps. Some numerical studies are included to illustrate the Allee effect and big bang local bifurcations.