Dynamics of a delayed stage-structured fishery management model with impulsive nonlinear harvesting and impulsive birth

Irrational fishing strategies have endangered numerous fish species. The density-dependent harvesting strategy has emerged as one of the potent approaches to address this issue. In this paper, we formulate a fishery management model incorporating the Beddington-DeAngelis functional response and delayed stage structure. The prey population is seasonal birth and impulsive nonlinear harvesting at distinct times. Initially, we show the positivity and the uniform boundedness of solutions in the system. By the comparison theorem of impulsive differential equations, we obtain the global attractivity conditions for the predator-extinction periodic solution. Sufficient conditions for the persistence of the system are derived via constructing the Lyapunov functions and applying other analytical methods. The numerical simulations demonstrate our findings and indicate that impulsive effects, impulsive period and maturation delay have significant influences on the dynamical behaviors of the system. These results provide certain theoretical guidance for sustainable fisheries.