A dynamic model describing heterotrophic culture of chorella and its stability analysis - Yan Zhang; Wanbiao Ma; Hai Yan; Yasuhiro Takeuchi (Mathematical Biosciences and Engineering)
Chlorella is an important species of microorganism, whichincludes about 10 species. Chlorella USTB01 is a strain ofmicroalga which is isolated from Qinghe River in Beijing and hasstrong ability in the utilization of organic compounds and wasidentified as Chlorella sp. (H. Yan etal, Isolation andheterotrophic culture of Chlorella sp., J. Univ. Sci.Tech. Beijing, 2005, 27:408-412). In this paper, based on thestandard Chemostat models and the experimental data on theheterotrophic culture of Chlorella USTB01, a dynamic modelgoverned by differential equations with three variables (Chlorella, carbon source and nitrogen source) is proposed. For themodel, there always exists a boundary equilibrium, i.e.Chlorella-free equilibrium. Furthermore, underadditional conditions, the model also has the positive equilibria,i.e., the equilibira for which Chlorella, carbon source andnitrogen source are coexistent. Then, local and global asymptoticstability of the equilibria of the model have been discussed.Finally, the parameters in the model are determined according to theexperimental data, and numerical simulations are given. Thenumerical simulations show that the trajectories of the modelfit the trends of the experimental data well.