Dynamics of a Fishery Management Model with Predation-Induced Fear Effect, Impulsive Nonlinear Harvesting Prey and Predator Seasonally Migrating Between Two Patches

This paper proposes a novel fishery management model that integrates three critical ecological factors: the prey (fish) fear effect, impulsive nonlinear harvesting, and predator seasonal migration. It is demonstrated that all solutions of the proposed system are uniformly ultimately bounded. We establish the conditions for the local and global asymptotic stability of the prey-extinction periodic solution, derive the permanence criteria for the system, and determine the threshold condition for prey extinction. Numerical simulations are conducted to validate the theoretical findings. These simulations also help identify the key parameters influencing the threshold condition and reveal the complex dynamics of the system. The results provide significant insights for fishery management, suggesting that regulating harvesting intensity and timing, as well as considering predator migration mortality, are crucial for sustaining fish populations and preventing overexploitation.