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Material recycling in a closed aquatic ecosystem. I. Nitrogen transformation cycle and preferential utilization of ammonium to nitrate by phytoplankton as an optimal control problem

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Abstract

A mathematical model of the nitrogen transformation cycle in an aquatic environment is studied. Using Pontryagin's maximum principle, a preferential utilization of ammonium to nitrate by phytoplankton is explained and verified by experimental data. A multiparameter bifurcation is given. The model was found to have four types of equilibrium sets. It is shown that a Hopf bifurcation may occur.

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  1. Department of Computer Science, Faculty of Natural Sciences, University of Education, Piaristická 10, 949 74, Nitra, Slovak Republic

    Tibor Kmeť

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  1. Tibor Kmeť
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Kmeť, T. Material recycling in a closed aquatic ecosystem. I. Nitrogen transformation cycle and preferential utilization of ammonium to nitrate by phytoplankton as an optimal control problem. Bltn Mathcal Biology 58, 957–982 (1996). https://doi.org/10.1007/BF02459492

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  • DOI: https://doi.org/10.1007/BF02459492

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