Dynamics of the Chemostat

Dynamics of the Chemostat: A Bifurcation Theory Approach

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Features

  • Provides a unified mathematical framework for analyzing dynamics of the chemostat
  • Presents a systematic and simple mathematical analysis using singularity theory and bifurcation techniques
  • Covers a variety of case studies ranging from simple microbial growth to dynamics of interacting species to dynamics with product formation
  • Addresses the connections between the design and control of the chemostat within the framework of singularity theory

Summary

A ubiquitous tool in mathematical biology and chemical engineering, the chemostat often produces instabilities that pose safety hazards and adversely affect the optimization of bioreactive systems. Singularity theory and bifurcation diagrams together offer a useful framework for addressing these issues. Based on the authors’ extensive work in this field, Dynamics of the Chemostat: A Bifurcation Theory Approach explores the use of bifurcation theory to analyze the static and dynamic behavior of the chemostat.

Introduction
The authors first survey the major work that has been carried out on the stability of continuous bioreactors. They next present the modeling approaches used for bioreactive systems, the different kinetic expressions for growth rates, and tools, such as multiplicity, bifurcation, and singularity theory, for analyzing nonlinear systems.

Application
The text moves on to the static and dynamic behavior of the basic unstructured model of the chemostat for constant and variable yield coefficients as well as in the presence of wall attachment. It then covers the dynamics of interacting species, including pure and simple microbial competition, biodegradation of mixed substrates, dynamics of plasmid-bearing and plasmid-free recombinant cultures, and dynamics of predator–prey interactions. The authors also examine dynamics of the chemostat with product formation for various growth models, provide examples of bifurcation theory for studying the operability and dynamics of continuous bioreactor models, and apply elementary concepts of bifurcation theory to analyze the dynamics of a periodically forced bioreactor.

Using singularity theory and bifurcation techniques, this book presents a cohesive mathematical framework for analyzing and modeling the macro- and microscopic interactions occurring in chemostats. The text includes models that describe the intracellular and operating elements of the bioreactive system. It also explains the mathematical theory behind the models.

Table of Contents

Introduction to Stability of Continuous Bioreactors
Introduction
Stability Studies of Continuous Bioreactors
Methodologies for Stability Analysis

Introduction to Bioreactors Models
Introduction
Continuous Bioreactors
Modeling Bioreactors
Kinetic Models for Cell Growth
Product Formation

Introduction to Stability and Bifurcation Theory
Introduction
Local Stability of Steady States
Steady State Multiplicity
Dynamic Bifurcation
Numerical Techniques
Singularity Theory

The Basic Model of Ideal Chemostat
Introduction
Process Model
Static Analysis
Dynamic Behavior for Constant Yield Coefficient
Dynamic Behavior for Variable Yield Coefficient
Concluding Remarks

The Chemostat with Wall Attachment
Introduction
Process Model
Static Analysis for Inhibition Kinetics
Static Analysis for Monod Growth
Quantification of the Stabilizing Effect of Wall Attachment
Concluding Remarks

Pure and Simple Microbial Competition
Introduction
Process Model
Static Bifurcation for Substrate Inhibition
Existence of Periodic Solutions
Monod Kinetics Model
Case of Sterile Feed
Concluding Remarks

Stability of Continuous Recombinant DNA Cultures
Introduction
Process Model
Dynamic Bifurcation
Applications to Monod/Haldane Substrate-Inhibited Kinetics
Implication of Resulting Dynamics
Concluding Remarks

Biodegradation of Mixed Substrates
Introduction
Bioreactor Model
Static Analysis
Concluding Remarks

Predator-Prey Interactions
Introduction
Bioreactor Model
Existence of Oscillatory Behavior
Construction of Operating Diagrams
Application to the Saturation Model
Application to the Multiple Saturation Model
Concluding Remarks

Ratio-Dependent Models
Introduction
Process Model
Existence of Periodic Solutions
Dynamics near the Washout Line
Bifurcation Diagrams
Concluding Remarks

Unstructured Models with Product Formation
Introduction
Type I Models

Models with Product Formation: Type II Models
Process Model
Static Analysis
Case Model 1
Case Model 2
Case Model 3

Models with Product Formation: Type III Models
Bioreactor Model
Static Singularities
Case Model 1
Case Model 2
Concluding Remarks

Operability of Nonideal Bioreactors
Introduction
Process Model
Static Singularities
Dynamic Bifurcation
Application to a Case Model
Concluding Remarks

Operability of Prefermentation of Cheese Culture
Introduction
Process Model
Static Multiplicity
Concluding Remarks

Biodegradation of Wastewater in Aerated Bioreactors
Introduction
Bioreactor Model
Steady-State Analysis
Dynamic Behavior of the Model
Performance Analysis
Concluding Remarks

Complex Dynamics in Activated Sludge Reactors
Introduction
Process Model
Results and Discussion
Concluding Remarks

Complex Dynamics in Forced Bioreactors
Introduction
Process Model and Presentations Techniques
Results and Discussion
Concluding Remarks

Appendix

Bibliography

Index

Author Bio(s)