Abstract
In this paper, the issue on the optimal harvesting of fish catching after eliminating toxin during the fish aquaculture is studied. Taking the aquaculture of bighead carp and silver carp as an example, considering the characteristics of the growth and the reproduction of prymnesiacee, and taking prymnesiacee toxin as the pollutant source, a harvesting model of fish aquaculture is built. The finite-time stability of the system is discussed. While the fish aquaculture and the elimination of the algae toxin targeted as pollutant source can be carried out simultaneously, an optimal harvesting method is made by the Pontryagin maximum principle, from which a general algorithm of the optimal harvesting solution can be obtained. The stimulation shows the effectiveness of the result.
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