The Theory of the Chemostat
Dynamics of Microbial Competition

Basic modelling, analysis and simulation of systems that have proven effective in real ecological applications.

Hal L. Smith (Author), Paul Waltman (Author)

9780521470278, Cambridge University Press

Hardback, published 27 January 1995

332 pages, 42 b/w illus. 5 tables
23.7 x 15.8 x 2.1 cm, 0.616 kg

"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

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.

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.

Subject Areas: Mathematical modelling [PBWH]