Abstract
This paper investigates a series of harvesting problems of a harvested predator-prey system with Holling type IV functional response. The bionomic equilibrium, the maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system are studied. It is proved that the MSTY does not exist under the independent harvesting mode, while it may be found with the same predator and prey harvesting efforts mode. By applying the Bang-Bang control and the singular control to the harvesting strategy, the optimal equilibrium state of the discussed system converges faster than that of the system utilizing a single harvesting strategy with the fixed harvesting effort. The MISER 3 software package is adopted to obtain the optimization schemes of two control problems by using the control parameterization method. The findings of our study provide a theoretical basis for biological resource management.
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