Global dynamics analysis of instantaneous harvest fishery model guided by weighted escapement strategy

Fisheries, forestry, and wildlife are precious renewable resource in the world, and reasonable exploitation and utilization are very important for human beings. Based on reasonable development consideration of fishery resources, in this work we proposed an instantaneous harvest fishery model, which is induced by the weighted escapement strategy. For the proposed model, we analyze the impact of fishing behavior on system dynamics under weighted escapement strategy, including the existence of predator-extinction periodic solution, coexistent order-q (q=1,2) periodic solution, and their stability. The existence threshold condition for the order-1 periodic solution provides a basis in the process for determining fishing period or frequency, and the stability threshold condition guarantees the robustness of the adapted instantaneous fishing strategy. Besides, in order to ensure a maximum of the revenue during the fishing process, we construct an optimization problem by introducing the cost of fishing and sales within a cycle. The correctness of the results are further verified through numerical simulations in MATLAB program.