A stage-structured model of population growth is proposed, where the time to maturity is itself state dependent. It is shown that under appropriate assumptions, all solutions are positive and bounded. Criteria for the existence of positive equilibria, and further conditions for the uniqueness of the equilibria are given. The stability of the equilibria are also discussed. In addition, an attracting region is determined for solutions, such that this region collapses to the unique positive equilibrium in the state-independent case.
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Aiello et al. (1992) studied this question.
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