Mathematical Biosciences and Engineering, 2011, 8(4): 1117-1133. doi: 10.3934/mbe.2011.8.1117.

Primary: 34K20; Secondary: 92C37.

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

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

1. Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083
2. Department of Biological Science and Technology, School of Chemical and Biological Engineering, University of Science and Technology Beijing, Beijing 100083
3. Graduate School of Science and Technology, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561

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.
  Article Metrics

Keywords carbon source; differential equation; Chlorella; nitrogen source; stability.

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


This article has been cited by

  • 1. Wei Wang, Wanbiao Ma, Hai Yan, Global Dynamics of Modeling Flocculation of Microorganism, Applied Sciences, 2016, 6, 8, 221, 10.3390/app6080221

Reader Comments

your name: *   your email: *  

Copyright Info: 2011, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved