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Model-Based Biological Control of the Chemostat

  • Neli S. Dimitrova
  • Mikhail I. Krastanov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

Abstract

In this paper we investigate a known competition model between two species in a chemostat with general (nonmonotone) response functions and distinct removal rates. Based on the competitive exclusion principle A. Rappaport and J. Harmand (2008) proposed the concept of the so called biological control. Here we present a generalization of this result.

Keywords

Biological Control Equilibrium Point Removal Rate Dilution Rate Competition Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Butler, G.J., Wolkowicz, G.S.K.: A mathematical model of the chemostat with a general class of functions describing nutrient uptake. SIAM Journ. Appl. Math. 45, 138–151 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    De Leenheer, P., Smith, H.: Feedback control for chemostat models. J. Math. Biol. 46, 48–70 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dimitrova, N., Krastanov, M.: Nonlinear adaptive control of a model of an uncertain fermentation process. Int. J. Robust Nonlinear Control 20, 1001–1009 (2010)MathSciNetGoogle Scholar
  4. 4.
    Golpalsamy, K.: Stability and oscillations in delay differential equations of population dynamics. Kluwer Academic Publishers, Dordrect (1992)Google Scholar
  5. 5.
    Harmand, J., Rapaport, A., Dochain, D., Lobry, C.: Microbial ecology and bioprocess control: opportunities and challehges. J. Proc. Control 18, 865–875 (2008)CrossRefGoogle Scholar
  6. 6.
    Hsu, S.-B.: A survey of construction Lyapunov functions for mathrmatical models in population biology. Taiwanese Journal of Mathematics 9(2), 151–173 (2005)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Li, B.: Global asymptotic behavior of the chemostat: general reponse functions and differential removal rates. SIAM Journ. Appl. Math. 59, 411–422 (1998)CrossRefGoogle Scholar
  8. 8.
    Maillert, L., Bernard, O., Steyer, J.-P.: Nonlinear adaptive control for bioreactors with unknown kinetics. Automatica 40, 1379–1385 (2004)CrossRefGoogle Scholar
  9. 9.
    Rapaport, A., Harmand, J.: Biological control of the chemostat with nonmonotonic response and different removal rates. Mathematical Biosciences and Engineering 5(3), 539–547 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Smith, H., Waltman, P.: The theory of the chemostat, dynamics of microbial competition. Cambridge University Press (1995)Google Scholar
  11. 11.
    Wolkowicz, G.S.K., Lu, Z.: Global dynamics of a mathematical model of competition in the chemostat: general response functions and differential remouval rates. SIAM J. Appl. Math. 52, 222–233 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Wolkowicz, G.S.K., Xia, H.: Global asymptotic behaviour of a chemostat model with discrete delays. SIAM J. Appl. Math. 57, 1281–1310 (1997)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Neli S. Dimitrova
    • 1
  • Mikhail I. Krastanov
    • 1
    • 2
  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Faculty of of Mathematics and InformaticsSofia UniversitySofiaBulgaria

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