Narrow Results

Toxic or allelopathic compounds liberated by toxin-producing phytoplankton (TPP) acts as a strong mediator in plankton dynamics. On an analysis of a set of phytoplankton biomass data that have been collected by our group in the northwest part of the Bay of Bengal, and by analysis of a three-component mathematical model under a constant as well as a stochastic environment, we explore the role of toxin-allelopathy in determining the dynamic behavior of the competing phytoplankton species. The overall results, based on analytical and numerical wings, demonstrate that toxin-allelopathy due to the TPP promotes a stable co-existence of those competitive phytoplankton that would otherwise exhibit competitive exclusion of the weak species. Our study suggests that TPP might be a potential candidate for maintaining the co-existence and diversity of competing phytoplankton species.

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.