The Theory of the Chemostat: Dynamics of Microbial Competition (Cambridge Studies in Mathematical Biology, Series Number 13)

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. Cover......Page 1 Title......Page 4 Copyright......Page 5 Dedication......Page 6 Contents......Page 8 Preface......Page 12 1 The Simple Chemostat......Page 18 1. Introduction......Page 0 2. Derivation of the Basic Equations of Growth......Page 20 3. Dynamical Systems......Page 24 4. Analysis of the Growth Equations......Page 30 5. Competition......Page 31 6. The Experiments......Page 36 7. Discussion......Page 37 2. Liapunov Theory......Page 45 3. General Monotone Response and Many Competitors......Page 47 4. Different Removal Rates......Page 51 5. Nonmonotone Uptake Functions......Page 54 6. Discussion......Page 59 1. Introduction......Page 60 2. The Model......Page 61 3. A Simple Food Chain......Page 64 4. Elementary Floquet Theory......Page 68 5. The Food Chain Continued......Page 70 6. Bifurcation from a Simple Eigenvalue......Page 76 7. Competing Predators......Page 82 8. Numerical Example......Page 85 9. A Long Food Chain......Page 86 10. Discussion......Page 88 1. Introduction......Page 95 2. The Model......Page 96 3. The Conservation Principle......Page 98 4. Rest Points and Stability......Page 103 5. Competition without an Interior Equilibrium......Page 108 6. Three-Dimensional Competitive Systems......Page 110 7. Competition with an Interior Equilibrium......Page 113 8. Discussion......Page 116 1. Introduction......Page 118 2. The Model......Page 120 3. The Set of Rest Points......Page 123 4. Growth without Competition......Page 128 5. Local Stability......Page 131 6. Order Properties......Page 136 7. Global Behavior of Solutions......Page 138 8. Numerical Example......Page 142 9. Discussion......Page 143 1. Introduction......Page 146 2. The Conservation Principle......Page 150 3. Growth without Competition......Page 154 4. Competition......Page 157 5. The Standard Gradostat......Page 168 6. Discussion......Page 174 1. Introduction......Page 176 2. Periodic Differential Equations......Page 179 3. The Conservation Principle......Page 181 4. Periodic Competitive Planar Systems......Page 186 5. Coexistence......Page 188 6. Discussion......Page 197 1. Introduction......Page 199 2. The Single-Population Growth Model......Page 200 3. The Competition Model......Page 205 4. The Conservation Principle......Page 209 5. Global Behavior of the Reduced System......Page 212 6. Competitive Exclusion......Page 220 7. Discussion......Page 223 1. Introduction......Page 225 2. The Single-Population Model......Page 226 3. Reduction to Ordinary Differential Equations......Page 231 4. Competition......Page 236 5. Average Cell Size......Page 239 6. The Conservation Principle......Page 242 7. The Steady-State Size Distribution......Page 243 8. Discussion......Page 245 2. The Unstirred Chemostat......Page 248 3. Delays in the Chemostat......Page 255 4. A Model of Plasmid-Bearing, Plasmid-Free Competition......Page 260 11 Open Questions......Page 265 Appendices......Page 270 A Matrices and Their Eigenvalues......Page 272 B Differential Inequalities......Page 278 C Monotone Systems......Page 285 D Persistence......Page 294 E Some Techniques in Nonlinear Analysis......Page 299 F A Convergence Theorem......Page 311 References......Page 316 Author index......Page 326 Subject index......Page 328 The chemostat is a basic piece of laboratory apparatus, yet it has begun to occupy 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 that take account of size structure, variable yields, and diffusion are also considered. The basic phenomena are modeled and analyzed using the dynamical systems approach. New 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. The chemostat is a basic piece of laboratory apparatus, yet it has begun to occupy 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. Mathematical models that take account of size structure, variable yields, and diffusion are also considered. The basic phenomena are modeled and analyzed using the dynamical systems approach. New directions for research and open problems are discussed. Six appendices provide an elementary description of the necessary mathematical tools.

basic Modelling, Analysis And Simulation Of Systems That Have Proven Effective In Real Ecological Applications.

"The best mathematical book I've ever read, Hal is truly the best".