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The Theory of the Chemostat
Dynamics of Microbial Competition

$66.00 USD

Part of Cambridge Studies in Mathematical Biology

  • Date Published: February 2011
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511834776

$ 66.00 USD
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About the Authors
  • The chemostat is a basic piece of laboratory apparatus, yet it has occupied an increasingly central role in ecological studies. The ecological environment created by a chemostat is one of the few completely controlled experimental systems for testing microbial growth and competition. As a tool in biotechnology, the chemostat plays an important role in bioprocessing. This book presents the theory of the chemostat as a model for larger ecological problems such as food chains, competition along a gradient, competition in the presence of an inhibitor, and the effects of time varying inputs. Models which take account of size structure, variable yields, and diffusion are also considered. The basic phenomena are modelled and analysed using the dynamical systems approach. Directions for research and open problems are discussed. Six appendices provide an elementary description of the necessary mathematical tools. Teachers, researchers, and students in applied mathematics, chemical engineering and ecology will find this book a welcome resource.

    • Mathematical models of competition
    • Dynamical systems approach
    • Mathematical techniques explained in detail
    • Future directions and open questions discussed
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    Product details

    • Date Published: February 2011
    • format: Adobe eBook Reader
    • isbn: 9780511834776
    • contains: 42 b/w illus. 5 tables
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    1. The simple chemostat
    2. The general chemostat
    3. Competition on three trophic levels
    4. The chemostat with an inhibitor
    5. The simple gradostat
    6. The general gradostat
    7. The chemostat with periodic washout rate
    8. Variable yield models
    9. A size-structured competition model
    10. New directions
    11. Open questions
    Appendix A. Matrices and their eigenvalues
    Appendix B. Differential inequalities
    Appendix C. Monotone systems
    Appendix D. Persistence
    Appendix E. Some techniques in nonlinear analysis
    Appendix F. A convergence theorem.

  • Authors

    Hal L. Smith, Arizona State University

    Paul Waltman, Emory University, Atlanta

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