Stability of a steady state of closed microecosystem «algae – heterotrophic bacteria»

Two models of closed microecosystem "algae–heterotrophic bacteria" are considered in this paper. Mathematical models are the Cauchy problem for system of non-linear ordinary differential equations. To develop models the Liebig's law of the minimum is consistently used for both specific rate of biomass growth and specific mortality rate of algae and bacteria cells. To describe the specific rate of substrate utilization by algae and bacteria the Andrew model (substrate inhibition) is used. It is assumed that carbon and nitrogen are main biogenic elements. Both models predict stationary state of microecosystem «Clorella vulgaris Pseudomonas sp.» that is in reasonable agreement with experimental data. Stability of the obtained stationary state is examined by means of Lyapunov's indirect method and Lyapunov's direct method based on the proposed form of Lyapunov function.