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Incorporating prey refuge into a predator-prey system with imprecise parameter estimates. (English) Zbl 1368.92161

Summary: This article is concerned with the optimal harvesting of a predator-prey model with a prey refuge and imprecise biological parameters. We consider the model under impreciseness and introduce a parametric functional form of an interval which differs from those of models with precise biological parameters. The existence of all possible equilibria and stability of system are discussed. The bionomic equilibrium of the model is analyzed. Also, the optimal harvesting policy is derived using Pontryagin’s maximal principle. Numerical simulations are presented to verify the feasibilities of our analytical results.

MSC:

92D25 Population dynamics (general)
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
49N90 Applications of optimal control and differential games
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