Mathematical Biosciences and Engineering, 2008, 5(3): 539-547. doi: 10.3934/mbe.2008.5.539.

Primary: 34D05, 34D23, 92D25; Secondary: 93C15.

Export file:

Format

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

Content

  • Citation Only
  • Citation and Abstract

Biological control of the chemostat with nonmonotonic response and different removal rates

1. UMR Analyse des Systèmes et Biométrie, INRA, EPI INRA/INRIA 'MODEMIC', 2 pl. Viala 34060 Montpellier
2. Laboratoire de Biotechnologie de l'Environnement, INRA, Avenue des Etangs, 11100 Narbonne

We show the global stabilization of the chemostat with nonmonotonic growth, adding a new species as a ''biological'' control, in presence of different removal rates for each species. This result is obtained by an extension of the Competitive Exclusion Principle in the chemostat, for the case of two species with different removal rates and at least one nonmonotonic response.
  Figure/Table
  Supplementary
  Article Metrics

Keywords global stabilization.; competition exclusion; chemostat

Citation: Alain Rapaport, Jérôme Harmand. Biological control of the chemostat with nonmonotonic response and different removal rates. Mathematical Biosciences and Engineering, 2008, 5(3): 539-547. doi: 10.3934/mbe.2008.5.539

 

This article has been cited by

  • 1. Jérôme Harmand, Alain Rapaport, Denis Dochain, Claude Lobry, Microbial ecology and bioprocess control: Opportunities and challenges, Journal of Process Control, 2008, 18, 9, 865, 10.1016/j.jprocont.2008.06.017
  • 2. Alain Rapaport, Some non-intuitive properties of simple extensions of the chemostat model, Ecological Complexity, 2018, 34, 111, 10.1016/j.ecocom.2017.02.003
  • 3. Alain Rapaport, Ihab Haidar, Jérôme Harmand, Global dynamics of the buffered chemostat for a general class of response functions, Journal of Mathematical Biology, 2015, 71, 1, 69, 10.1007/s00285-014-0814-7
  • 4. , , The Chemostat, 2017, 217, 10.1002/9781119437215.biblio
  • 5. Nahla Abdellatif, Radhouane Fekih-Salem, Tewfik Sari, Competition for a single resource and coexistence of several species in the chemostat, Mathematical Biosciences and Engineering, 2016, 13, 4, 631, 10.3934/mbe.2016012
  • 6. Tewfik Sari, Competitive Exclusion for Chemostat Equations with Variable Yields, Acta Applicandae Mathematicae, 2013, 123, 1, 201, 10.1007/s10440-012-9761-8
  • 7. A. Rapaport, I. Haidar, J. Harmand, The buffered chemostat with non-monotonic response functions, IFAC Proceedings Volumes, 2013, 46, 23, 181, 10.3182/20130904-3-FR-2041.00039
  • 8. Mieczyslaw Metzger, Piotr Skupin, Concept of food-chain control in the bioreactor fed with a mixture of substrates, Aquaculture, 2017, 467, 127, 10.1016/j.aquaculture.2016.04.027
  • 9. Neli S. Dimitrova, Mikhail I. Krastanov, New result on the model-based biological control of the chemostat, Applied Mathematics and Computation, 2014, 237, 686, 10.1016/j.amc.2014.03.127
  • 10. Miaomiao Gao, Daqing Jiang, Tasawar Hayat, The threshold of a chemostat model with single-species growth on two nutrients under telegraph noise, Communications in Nonlinear Science and Numerical Simulation, 2019, 75, 160, 10.1016/j.cnsns.2019.03.027
  • 11. Neli S. Dimitrova, Mikhail I. Krastanov, , Numerical Analysis and Its Applications, 2013, Chapter 25, 239, 10.1007/978-3-642-41515-9_25
  • 12. Francis Mairet, Jean-Luc Gouzé, , Formal Methods in Macro-Biology, 2014, Chapter 5, 47, 10.1007/978-3-319-10398-3_5
  • 13. Tewfik Sari, Frederic Mazenc, Global dynamics of the chemostat with different removal rates and variable yields, Mathematical Biosciences and Engineering, 2011, 8, 3, 827, 10.3934/mbe.2011.8.827
  • 14. Emna Krichen, Alain Rapaport, Emilie Le Floc’h, Eric Fouilland, Demonstration of facilitation between microalgae to face environmental stress, Scientific Reports, 2019, 9, 1, 10.1038/s41598-019-52450-9
  • 15. J. Harmand, A. Rapaport, T. Nidelet, About overyielding with mixed cultures in batch processes, IFAC-PapersOnLine, 2019, 52, 26, 163, 10.1016/j.ifacol.2019.12.252

Reader Comments

your name: *   your email: *  

Copyright Info: 2008, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved