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.
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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)
De Leenheer, P., Smith, H.: Feedback control for chemostat models. J. Math. Biol. 46, 48–70 (2003)
Dimitrova, N., Krastanov, M.: Nonlinear adaptive control of a model of an uncertain fermentation process. Int. J. Robust Nonlinear Control 20, 1001–1009 (2010)
Golpalsamy, K.: Stability and oscillations in delay differential equations of population dynamics. Kluwer Academic Publishers, Dordrect (1992)
Harmand, J., Rapaport, A., Dochain, D., Lobry, C.: Microbial ecology and bioprocess control: opportunities and challehges. J. Proc. Control 18, 865–875 (2008)
Hsu, S.-B.: A survey of construction Lyapunov functions for mathrmatical models in population biology. Taiwanese Journal of Mathematics 9(2), 151–173 (2005)
Li, B.: Global asymptotic behavior of the chemostat: general reponse functions and differential removal rates. SIAM Journ. Appl. Math. 59, 411–422 (1998)
Maillert, L., Bernard, O., Steyer, J.-P.: Nonlinear adaptive control for bioreactors with unknown kinetics. Automatica 40, 1379–1385 (2004)
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)
Smith, H., Waltman, P.: The theory of the chemostat, dynamics of microbial competition. Cambridge University Press (1995)
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)
Wolkowicz, G.S.K., Xia, H.: Global asymptotic behaviour of a chemostat model with discrete delays. SIAM J. Appl. Math. 57, 1281–1310 (1997)
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Dimitrova, N.S., Krastanov, M.I. (2013). Model-Based Biological Control of the Chemostat. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_25
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DOI: https://doi.org/10.1007/978-3-642-41515-9_25
Publisher Name: Springer, Berlin, Heidelberg
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