Analysis of a Model Representing Stage-Structured Population Growth with State-Dependent Time Delay

TLDR

The study proposes a stage‑structured population growth model with state‑dependent maturation time. The authors provide criteria for existence and uniqueness of positive equilibria in the model. Under suitable assumptions, solutions remain positive and bounded, equilibria are stable, and an attracting region leads to the unique positive equilibrium when the delay is state‑independent.

Abstract

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.