On the dynamics of a linear-hyperbolic population model with Allee effect and almost sure extinction

Abstract

This paper considers a biological model in which two stages of the population, adults and preadults, are modeled by a Beverton-Holt type function and a logistic-type function. Two new models are proposed, each with an additional parameter representing the compensation. This new parameter is introduced in adult and juvenile populations. As a result, the Allee effect is observed in both models. The scenario of almost sure extinction can appear when the dynamic is chaotic enough.