Dynamics of a stage-structured population model incorporating a state-dependent maturation delay

In 1992, Aiello, Freedman and Wu proposed a mathematical model of certain marine populations in which the time from birth to maturity is directly related to the number of individuals present. Individuals mature more quickly when there are fewer of them around. We propose an alternative model allowing a non-monotone birth function of the kind seen in other frequently studied population models. We study the dynamics of our model both analytically and numerically, and we present results on positivity and boundedness, existence and local stability of equilibria, global stability of the extinction state under certain conditions, and existence of periodic solutions. The qualitative form of the latter and their sensitivity to parameters are discussed.