In this paper, we propose an aquaculture management model with stage structure, intraspecific cooperation, refuge effect, and nonlinearly impulsive releasing. The global asymptotic stability of the periodic solution for the subsystem of the system was analyzed via the Jury criterion and the Banach contraction mapping principle. Additionally, through the theory of impulsive differential equations, the conditions for the global asymptotic stability of the prey-vanishing periodic solution and for the permanence of the system were acquired. Finally, numerical simulations were utilized to validate the theoretical results. In addition, key parameters affecting the persistence condition $B_0$ were identified via comparative and sensitivity analysis. Moreover, abundant dynamical behaviors such as period bifurcation and chaos were identified through bifurcation diagrams.

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.

Ecological aquaculture represents an important approach for maintaining sustainable economic income. Unreasonable aquaculture may result in resource wastage and population extinction. Human activities and behaviors such as predation among populations make the ecosystem very complex. Thus, seeking an appropriate intervention strategy is a favorable measure to overcome this situation. In this paper, we present a novel ecological aquaculture management model with stage-structure and impulsive nonlinear releasing larval predators. The sufficient conditions for the prey and the predators coexistence as well as global stability of a prey-vanishing periodic solution were obtained using the Floquet theorem and other analytic tactics. Subsequently, we verified our findings using mathematical software. We also found a system with a nonlinear impulse exhibiting rich dynamical properties by drawing bifurcation parameter graphs. These findings provide a firm theoretical basis for managing ecological aquaculture.

In this study, we propose and analyze a Susceptible-Infected (SI) epidemic model applied to pest management, focusing on the nonlinear release of infected pests and an instantaneous pulse of pesticide spraying. Additionally, the mortality rates of both susceptible and infected pests following the pesticide application are modeled as non-instantaneous pulses. Utilizing the comparison theorem for pulse differential equations and Floquet theory, we derive a threshold condition for the eradication of susceptible pests. We also demonstrate that all solutions are uniformly ultimately bounded. Furthermore, we establish conditions for the globally asymptotic stability of the pest-free boundary periodic solution and the permanence of the system. Finally, numerical simulations are conducted to verify the theoretical findings, and the key parameters affecting the pest extinction threshold were obtained, thereby providing a solid theoretical basis for the development of effective pest management strategies.