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  5. Mathematical model of eutrophications influence to the structure and dynamics of relations in the lake zooplankton

Mathematical model of eutrophications influence to the structure and dynamics of relations in the lake zooplankton

О. Vуsotska, А. Bykh, A. Pecherska, Yu. Bespalov, R. Matviienko, A.Tarasova
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Description: One of the aspects of the loss the stability by aquatic ecosystem is the massive development of toxic cyanobacteria, which were not previously observed in this ecosystem. The variety of aquatic ecosystems types that can undergo eutrophication with the massive development of cyanobacteria is quite large. There is no satisfactory solution to the question of an adequate laboratory model of an aquatic ecosystem with the massive development of toxic cyanobacteria. These circumstances make it a topical issue to develop mathematical methods and information technologies for identifying and analyzing the risk factors for the development of toxic cyanobacteria in eutrophied reservoirs. Such factors include the structure of relationships and the dynamics of zooplankton of the analyzed ecosystems.Relevance of the research of eutrophications influence to the structure and dynamics of relations in the lake zooplankton using mathematical modeling substantiated in the paper. As a result of mathematical modeling using DMDS, idealized trajectories of the analyzed ecosystem are obtained. The resulting trajectory reflect the dynamics of the number of such groups of zooplankton as: Rotatoria, Daphnia, Diaptomidae and Cyclops, in different periods of eutrophication of Lake Sevan. The analysis of the trajectories of the system revealed that in the stable and unstable periods of eutrophication of Lake Sevan, combinations of values of the numbers of the analyzed groups of zooplankton differ. In the stable period, the maximum number of steps is observed with the coincidence of the minimum values of the number of Rotatoria and Daphnia. In the unstable period, the maximum number of steps is observed with the coincidence of the maximum values of the number of Rotatoria and Diaptomidae.It is proposed to use the difference between the normalized values of the abundance of groups of zooplankton, the combination of the values of whose numbers differ in stable and unstable periods of the aquatic ecosystem, as system parameters. Obtained results can be used in the development of an information system for determining the risk of developing toxic cyanobacteria in a wide class of eutrophied reservoirs.

Keywords: dynamic system, zooplankton, mathematical modeling, system parameters, toxic cyanobacteria, eutrophication


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