Dynamics of Nonautonomous Chemostat Models

  • Tomás CaraballoEmail author
  • Xiaoying Han
  • Peter E. Kloeden
  • Alain Rapaport
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 30)


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.


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.



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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Tomás Caraballo
    • 1
    Email author
  • Xiaoying Han
    • 2
  • Peter E. Kloeden
    • 3
    • 4
  • Alain Rapaport
    • 5
    • 6
  1. 1.Dpto. Ecuaciones Diferenciales y Análisis NuméricoUniversidad de SevillaSevillaSpain
  2. 2.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA
  3. 3.School of Mathematics and StatisticsHuazhong University of Science & TechnologyWuhanChina
  4. 4.Felix-Klein-Zentrum Für MathematikTU KaiserslauternKaiserslauternGermany
  5. 5.UMR INRA/SupAgro MISTEAMontpellierFrance
  6. 6.MODEMIC TeamINRIASophia-AntipolisFrance

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