Abstract
Considering the uncertainty of kelp–abalone–sea cucumber population, an interval model of carbon sink fisheries with multi-trophic levels is proposed. The equilibria of the model are identified and the corresponding stabilities are discussed. And the existence of bionomic equilibrium of the model is investigated. Next the optimal controller is designed to obtain the optimal harvest using Pontryagin’s maximum principle. Numerical simulations are carried to prove the results.
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