Generalized model of closed microecosystem «alga - micro-consumers»

Abstract

Model of closed microecosystem “alga-micro-consumers” is proposed in this paper. Mathematical model is the Cauchy problem for system of nonlinear ordinary differential equations. To develop the model Liebig's law of the minimum is consistently used for both specific rate of biomass growth and specific death rate of alga and micro-consumers cells. To describe the specific rate of substrate utilization by alga and micro-consumer the Andrew model (substrate inhibition) is used. It is assumed that specific death rate of alga and micro-consumer cells increases with decreasing substrate concentration. It is also assumed that carbon and nitrogen are main biogenic elements, and in the system they are in the form of mineral substrate and biological substrate. To verify the proposed model experimental data for microecosystems « Chlorella vulgaris–Pseudomonas sp» and «Chlorella vulgaris–Pseudomonas sp–Mycobacterium rubrum » are used. These systems were studied in laboratory conditions, and concentrations of elements of microecosystems in stationary state were obtained. Parameters of functions describing specific rate of utilization of biogenic elements were derived from experimental data for growth kinetics of alga and bacteria. Concentration of the biomass in stationary state obtained with the use of the proposed model is in reasonable agreement with experimental data.