A dynamic model describing heterotrophic culture of Chlorella and its stability analysis

Chlorella is an important species of microorganism, which includes about 10 species. Chlorella USTB01 is a strain of microalga which is isolated from Qinghe River in Beijing and has strong ability in the utilization of organic compounds and was identified as Chlorella sp. (H. Yan et al, Isolation and heterotrophic culture of Chlorella sp., J. Univ. Sci. Tech. Beijing, 2005, 27:408-412). In this paper, based on the standard Chemostat models and the experimental data on the heterotrophic culture of Chlorella USTB01, a dynamic model governed by differential equations with three variables (Chlorella, carbon source and nitrogen source) is proposed. For the model, there always exists a boundary equilibrium, i.e. Chlorella-free equilibrium. Furthermore, under additional conditions, the model also has the positive equilibria, i.e., the equilibira for which Chlorella, carbon source and nitrogen source are coexistent. Then, local and global asymptotic stability of the equilibria of the model have been discussed. Finally, the parameters in the model are determined according to the experimental data, and numerical simulations are given. The numerical simulations show that the trajectories of the model fit the trends of the experimental data well.