Abstract
We study the optimal harvesting policy for fishery in the marine protected and unreserved areas. In the literature, it is generally assumed that the fish population follows a concrete growth law. In contrast, we consider an abstract model with migration from the reserved area to the unreserved one. Then we examine and analyze the existence and stability of a nontrivial equilibrium point of the model. We also discuss the bionomic equilibrium. After that, we use the Pontryagin maximum principle to obtain the optimal harvest policy, where, instead of the well-known Hamiltonian function, we use the current Hamiltonian function to ease the calculation. Finally, we give some numerical examples to further illustrate our statements, where we also find that in practice the impreciseness of the parameters can influence the existence of the system positive equilibrium.
Highlights
1 Introduction A marine protected area (MPA) is essentially a space in the ocean where human activities are more strictly regulated than the surrounding waters, to parks we have on land
At the end of this section, we prove the existence of bionomic equilibrium of the model and study the optimal harvesting policy
5 Discussion In this work, we studied the optimal harvesting of fishery in the marine reserved area and its adjacent area
Summary
A marine protected area (MPA) is essentially a space in the ocean where human activities are more strictly regulated than the surrounding waters, to parks we have on land. These places are given special protections for natural or historic marine resources by local, state, territorial, native, regional, or national authorities. Some 72 percent of the marine protected area will be a “no-take” zone, where all fishing is forbidden, whereas other areas will allow some harvesting of fish and krill for scientific research. Reserves or “no-take” areas [2] often form a part of larger MPAs that have less protection and may include areas that allow
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