Optimal harvesting of an abstract population model with interval biological parameters

Abstract

AbstractWe 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.