A Structured Predator–Prey Model with a State-Dependent Maturation Period

In this paper, we introduce a novel predator–prey model that accounts for the impact of the juvenile predator population size during its mature period. The model incorporates a nonlinear feedback growth rate, and we analyze its dynamics by transforming it into three forms using the characteristic method and time scales. We establish global threshold dynamics of the system based on the net reproductive number of predators, as well as criteria for the local asymptotic stability of the coexistence equilibrium. To validate these theoretical findings, numerical simulations are then implemented, enabling direct comparison between the model’s behavior and that of its constant-delay equivalent. Our results provide valuable insights into the effects of state-dependent maturation delay on predator–prey dynamics, and we offer a framework for comprehending and predicting population predation in structured populations.