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Continuous and Distributed Systems II pp 103–120Cite as

Dynamics of Nonautonomous Chemostat Models

Part of the Studies in Systems, Decision and Control book series (SSDC,volume 30)

Abstract

Chemostat models have a long history in the biological sciences as well as in biomathematics. Hitherto most investigations have focused on autonomous systems, that is, with constant parameters, inputs, and outputs. In many realistic situations these quantities can vary in time, either deterministically (e.g., periodically) or randomly. They are then nonautonomous dynamical systems for which the usual concepts of autonomous systems do not apply or are too restrictive. The newly developing theory of nonautonomous dynamical systems provides the necessary concepts, in particular that of a nonautonomous pullback attractor. These will be used here to analyze the dynamical behavior of nonautonomous chemostat models with or without wall growth, time-dependent delays, variable inputs and outputs. The possibility of overyielding in nonautonomous chemostats will also be discussed.

Keywords

  • Delay Differential Equation
  • Random Dynamical System
  • Random Attractor
  • Wall Growth
  • Pullback Attractor

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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Acknowledgments

This work has been partially supported by the Spanish Ministerio de Economía y Competitividad project MTM2011-22411 and the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía) under grant 2010/FQM314 and Proyecto de Excelencia P12-FQM-1492.

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Authors and Affiliations

  1. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080, Sevilla, Spain

    Tomás Caraballo

  2. Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, 36849, USA

    Xiaoying Han

  3. School of Mathematics and Statistics, Huazhong University of Science & Technology, Wuhan, 430074, China

    Peter E. Kloeden

  4. Felix-Klein-Zentrum Für Mathematik, TU Kaiserslautern, 67663, Kaiserslautern, Germany

    Peter E. Kloeden

  5. UMR INRA/SupAgro MISTEA, 2 Place Viala, 34060, Montpellier, France

    Alain Rapaport

  6. MODEMIC Team, INRIA, rte des Lucioles, 06 902, Sophia-Antipolis, France

    Alain Rapaport

Authors
  1. Tomás Caraballo
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  2. Xiaoying Han
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  3. Peter E. Kloeden
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  4. Alain Rapaport
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Corresponding author

Correspondence to Tomás Caraballo .

Editor information

Editors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Viktor A. Sadovnichiy

  2. Kiev Polytechnic Institute, National Technical University Ukraine, Kiev, Ukraine

    Mikhail Z. Zgurovsky

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Caraballo, T., Han, X., Kloeden, P.E., Rapaport, A. (2015). Dynamics of Nonautonomous Chemostat Models. In: Sadovnichiy, V., Zgurovsky, M. (eds) Continuous and Distributed Systems II. Studies in Systems, Decision and Control, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-19075-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-19075-4_6

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