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 etal, 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.
Citation: Yan Zhang, Wanbiao Ma, Hai Yan, Yasuhiro Takeuchi. A dynamic model describing heterotrophic culture of chorella and its stability analysis[J]. Mathematical Biosciences and Engineering, 2011, 8(4): 1117-1133. doi: 10.3934/mbe.2011.8.1117
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Abstract
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 etal, 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.