Complex dynamics of a fishery model: Impact of the triple effects of fear, cooperative hunting and intermittent harvesting

In natural ecosystems, predators often live in groups and have evolved cooperative hunting behaviors over time. This cooperative behavior on the one hand increases the success rate of the prey, but it also leads to the fear response of prey to predators, thereby affecting the reproduction rate of prey populations. In the current study, we put forward a fishery model for renewable aquatic resource with dual effects of fear and cooperative hunting, and investigate the impact of fear level and cooperative hunting intensity on the dynamics of the model. The analysis shows that the level of fear and the intensity of cooperative hunting can affect the existence and number of coexisting equilibria. Secondly, from the perspective of rational exploitation of fishery resources, we adopt a state-feedback intermittent fishing strategy, which fully considers the current status of the target species and avoids the impact of irrational fishing on the ecosystem. We investigate the dynamic behavior of the fishery model under discontinuous fishing model, including the existence and stability of predator-extinction periodic solution and co-existence order-1 and order-2 periodic solutions under different fishing thresholds, which not only provides a possibility to fishing species according to the period, but also ensures a certain robustness of the fishing strategy. Finally, the main results are verified by numerical simulations using MATLAB program and their biological implications are discussed.