Dynamics of an Aquaculture Model With Impulsive Harvesting of Predators and Density-Dependent Nonlinear Release of Prey

In this article, we propose an aquaculture model with impulsive harvesting predator and density-dependent nonlinear releasing prey. By taking advantage of the stroboscopic map and Cardano’s formula, the predator-extinction periodic solution is derived for three different cases. The conditions for the global asymptotic stability of the predator-extinction periodic solution and for the permanence of the model are obtained using Floquet theory and the comparison theorem of impulsive differential equations, respectively. Furthermore, using bifurcation theory with the impulsive period as a parameter, we establish conditions under which the system bifurcates from a predator-extinction periodic solution to a positive periodic solution, signifying prey–predator coexistence as the impulsive period crosses a critical value. To demonstrate the main results and investigate the effects of the impulsive control period and the maximum prey release amount on the dynamic behavior of the investigated model, numerical simulations are conducted. The results show that both the impulsive period and the maximum prey release amount significantly affect the dynamic behavior of the model. These findings provide a reliable theoretical basis for practical aquaculture management.