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The Theory of the Chemostat: Dynamics of Microbial Competition

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

Series: Cambridge Studies in Mathematical Biology Volume: 13

By: Hal L Smith(Author), Paul Waltman(Author)

313 pages, illustrations, tables

Cambridge University Press

Hardback | Feb 1995 | #47285 | ISBN: 0521470277
Availability: Usually dispatched within 6 days Details
NHBS Price: £108.00 $146/€122 approx

About this book

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. The Theory of the Chemostat 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 The Theory of the Chemostat a welcome resource.

"[...] a logically ordered and mathematically rigorous explication of the chemostat theory in terms of ODEs [...] the book can be recommended as a valuable source of reference for students, teachers, and researchers [...]"
- D.O. Logofet, Mathematical Reviews

"If you work with microbial systems and contend with dynamic and competition phenomena, this book will serve as a good, concise reference for problemas and approaches that are applicable to many fundamental and applied areas [...] Getting a copy for yourself or in the library would be worthwhile."
- Michael Domach, Journal of the American Chemical Society

"I [...] enthusiastically recommend this monograph to both scientists and mathematicians planning to do research related to chemostat-like models, for whom I think it will be indispensable."
- Gail S.K. Wolkowicz, Bulletin of Mathematical Biology

"The Theory of Chemostat by Smith and Waltman, two of the leading authorities on the thoery of the chemostat, provides an outstanding introduction to this thoery. Starting from the simplest models of the well-stirred chemostat, they lead the reader from the basic theory, through many of its elaborations, up to the frontiers of current research and many open questions and unsolved problems [...] This well-written, well-organized book is destined to become a classic in mathematical biology."
- J.M. Cushing, SIAM Review


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

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