Dynamical analysis of a differential-algebraic bioeconomic model with stage structure and maturation delay

In this paper, a stage structured prey-predator-resource model with maturation delay is established, where resource biomass is harvested. Persistence of solutions of model system is studied. Dynamic analysis of model system with maturation delay is investigated, which shows that interior equilibrium loses its stability at some critical values of maturation delay and economic interest of harvesting. Further discussion shows that maturation delay to preserve stability increases with the introduction of harvest effort into bioeconomic prey-predator-resource model.