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Mathematical Biosciences and Engineering (MBE)
 

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

Pages: 1117 - 1133, Volume 8, Issue 4, October 2011      doi:10.3934/mbe.2011.8.1117

 
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Yan Zhang - Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China (email)
Wanbiao Ma - Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China (email)
Hai Yan - Department of Biological Science and Technology, School of Chemical and Biological Engineering, University of Science and Technology Beijing, Beijing 100083, China (email)
Yasuhiro Takeuchi - Graduate School of Science and Technology, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan (email)

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.

Keywords:  Chlorella, carbon source, nitrogen source, differential equation, stability.
Mathematics Subject Classification:  Primary: 34K20; Secondary: 92C37.

Received: October 2009;      Accepted: October 2010;      Available Online: August 2011.

 References