On a population model with density dependence and Allee effect

We study the dynamics of a discrete model with two different stages of the population, the pre-adult stage governed by a Beverton–Holt-type map and the adult stage by a γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma$$\end{document}-Ricker map. The composition of both maps gives the dynamics. The existence of the Allee effect is easily observed. We check that the model can evolve from a sure extinction to complicated dynamics. The presence of an almost sure extinction is proved to exist when the dynamical complexity is the highest possible.