Dynamics of the Chemostat: A Bifurcation Theory Approach, 1st Edition (Paperback) book cover

Dynamics of the Chemostat

A Bifurcation Theory Approach, 1st Edition

By Abdelhamid Ajbar, Khalid Alhumaizi

Chapman and Hall/CRC

368 pages | 145 B/W Illus.

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Description

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

About the Authors

Abdelhamid Ajbar is a professor in the Department of Chemical Engineering at King Saud University. He earned a Ph.D. in chemical engineering from the University of Notre Dame. His research interests encompass the analysis, design, and control of chemical and biochemical systems as well as the applications of chaos theory to study hydrodynamics of multiphase reactors.

Khalid Alhumaizi is a professor in the Department of Chemical Engineering at King Saud University. He earned a Ph.D. in chemical engineering from the University of Minnesota. He also co-authored (with the late R. Aris) the book Surveying a Dynamical System: A Study of the Gray-Scott Reaction in a Two-Phase Reactor. His research interests include process modeling and simulation and nonlinear dynamics.

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
SCI010000
SCIENCE / Biotechnology