Qualitative analysis of exponential power rate fishery model and complex dynamics guided by a discontinuous weighted fishing strategy

A global data set for 2260 communities of large mammals, invertebrates, plants, and plankton indicated that the predator and prey densities follow a general scaling law (Hotton et al., 2015). Motivated by this study, a predator–prey model for fisheries with an exponential power rate and Ivlev-type functional response is proposed in this work. The influence of exponential factor on the stability of the coexistence equilibrium is investigated. In addition, from the perspective of scientific and reasonable exploitation and utilization of fishery resources, a weighted fishing strategy is introduced into the model, the complex dynamics induced by the weighted harvesting activity is analyzed, which includes the existence of predator-extinction periodic solution, positive order-1 periodic solution, and their stability. The existence threshold condition provides a basis in the process for determining fishing period or frequency, and the stability threshold condition guarantees the robustness of the adapted weighted fishing strategy. In addition, an optimization problem is formulated to ensure a maximum of the revenue during the fishing process by introducing the cost of fishing and sales within one fishing cycle. At the end of the study, numerical simulations and optimization are implemented in MATLAB program to verify the theoretical results and a conclusion is presented from the perspective of biological significance. •This work proposes a predator–prey model for fisheries with an exponential power rate.•Influence of exponential factor on the stability of the coexistence equilibrium is investigated.•Complex dynamics induced by the weighted harvesting activity is analyzed.•Optimization process provides a way to determine the optimal harvesting strategy.