1st Edition

Dynamics of the Chemostat A Bifurcation Theory Approach

By Abdelhamid Ajbar, Khalid Alhumaizi Copyright 2012
    368 Pages 145 B/W Illustrations
    by Chapman & Hall

    368 Pages 145 B/W Illustrations
    by Chapman & Hall

    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.

    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

    Biography

    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.