The Chemostat
The Chemostat

Author: Jérôme Harmand

Publisher: John Wiley & Sons

Published: 2017-07-19

Total Pages: 246

ISBN-13: 1119437121

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Invented by J. Monod, and independently by A. Novick and L. Szilard, in 1950, the chemostat is both a micro-organism culturing device and an abstracted ecosystem managed by a controlled nutrient flow. This book studies mathematical models of single species growth as well as competition models of multiple species by integrating recent work in theoretical ecology and population dynamics. Through a modeling approach, the hypotheses and conclusions drawn from the main mathematical results are analyzed and interpreted from a critical perspective. A large emphasis is placed on numerical simulations of which prudent use is advocated. The Chemostat is aimed at readers possessing degree-level mathematical knowledge and includes a detailed appendix of differential equations relating to specific notions and results used throughout this book.

The Theory of the Chemostat
The Theory of the Chemostat

Author: Hal L. Smith

Publisher: Cambridge University Press

Published: 1995-01-27

Total Pages: 334

ISBN-13: 9780521470278

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

The Chemostat
The Chemostat

Author: Jérôme Harmand

Publisher: John Wiley & Sons

Published: 2017-08-07

Total Pages: 244

ISBN-13: 1786300435

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Invented by J. Monod, and independently by A. Novick and L. Szilard, in 1950, the chemostat is both a micro-organism culturing device and an abstracted ecosystem managed by a controlled nutrient flow. This book studies mathematical models of single species growth as well as competition models of multiple species by integrating recent work in theoretical ecology and population dynamics. Through a modeling approach, the hypotheses and conclusions drawn from the main mathematical results are analyzed and interpreted from a critical perspective. A large emphasis is placed on numerical simulations of which prudent use is advocated. The Chemostat is aimed at readers possessing degree-level mathematical knowledge and includes a detailed appendix of differential equations relating to specific notions and results used throughout this book.

Dynamics of the Chemostat
Dynamics of the Chemostat

Author: Abdelhamid Ajbar

Publisher: CRC Press

Published: 2011-08-09

Total Pages: 370

ISBN-13: 1439867143

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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.

Polymicrobial Diseases
Polymicrobial Diseases

Author: Kim A. Brogden

Publisher:

Published: 2002

Total Pages: 460

ISBN-13:

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Polymicrobial diseases, those involving more than one etiologic agent, are more common than is generally realized and include respiratory diseases, gastroenteritis, conjunctivitis, keratitis, hepatitis, periodontal diseases, multiple sclerosis, genital infections, intra -- abdominal infections, and pertussis.

Introduction to Polyphasic Dispersed Systems Theory
Introduction to Polyphasic Dispersed Systems Theory

Author: Jacques Thierie

Publisher: Springer

Published: 2015-12-30

Total Pages: 210

ISBN-13: 3319278533

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This book introduces a new paradigm in system description and modelling. The author shows the theoretical and practical successes of his approach, which involves replacing a traditional uniform description with a polyphasic description. This change of perspective reveals new fluxes that are cryptic in the classical description. Several case studies are given in this book, which is of interest of those working with biotechnology and green chemistry.

Adaptive Diversification
Adaptive Diversification

Author: Michael Doebeli

Publisher: Princeton University Press

Published: 2011-08-01

Total Pages: 346

ISBN-13: 1400838932

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Understanding the mechanisms driving biological diversity remains a central problem in ecology and evolutionary biology. Traditional explanations assume that differences in selection pressures lead to different adaptations in geographically separated locations. This book takes a different approach and explores adaptive diversification--diversification rooted in ecological interactions and frequency-dependent selection. In any ecosystem, birth and death rates of individuals are affected by interactions with other individuals. What is an advantageous phenotype therefore depends on the phenotype of other individuals, and it may often be best to be ecologically different from the majority phenotype. Such rare-type advantage is a hallmark of frequency-dependent selection and opens the scope for processes of diversification that require ecological contact rather than geographical isolation. Michael Doebeli investigates adaptive diversification using the mathematical framework of adaptive dynamics. Evolutionary branching is a paradigmatic feature of adaptive dynamics that serves as a basic metaphor for adaptive diversification, and Doebeli explores the scope of evolutionary branching in many different ecological scenarios, including models of coevolution, cooperation, and cultural evolution. He also uses alternative modeling approaches. Stochastic, individual-based models are particularly useful for studying adaptive speciation in sexual populations, and partial differential equation models confirm the pervasiveness of adaptive diversification. Showing that frequency-dependent interactions are an important driver of biological diversity, Adaptive Diversification provides a comprehensive theoretical treatment of adaptive diversification.

Time Lags in Biological Models
Time Lags in Biological Models

Author: N. MacDonald

Publisher: Springer Science & Business Media

Published: 2013-03-08

Total Pages: 122

ISBN-13: 3642931073

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In many biological models it is necessary to allow the rates of change of the variables to depend on the past history, rather than only the current values, of the variables. The models may require discrete lags, with the use of delay-differential equations, or distributed lags, with the use of integro-differential equations. In these lecture notes I discuss the reasons for including lags, especially distributed lags, in biological models. These reasons may be inherent in the system studied, or may be the result of simplifying assumptions made in the model used. I examine some of the techniques available for studying the solution of the equations. A large proportion of the material presented relates to a special method that can be applied to a particular class of distributed lags. This method uses an extended set of ordinary differential equations. I examine the local stability of equilibrium points, and the existence and frequency of periodic solutions. I discuss the qualitative effects of lags, and how these differ according to the choice of discrete or distributed lag. The models studied are drawn from the population dynamiCS of single species (logistic growth, the chemostat) and of interacting pairs of species (predation, mutualism), from cell population dynamiCS (haemopoiesis) and from biochemical kinetics (the Goodwin oscillator). The last chapter is devoted to a population model employing difference equations. All these models include non-linear terms.

Plankton Regulation Dynamics
Plankton Regulation Dynamics

Author: Norbert Walz

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 310

ISBN-13: 3642778046

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Continuous cultures, i.e. chemostats with an continuous dilution rate, are model ecosystems for the study of general regulation principles in plankton communities. Further to an introduction, general continuous culture methods and especially the characteristics of rotifer continuousculture systems are presented. Sections on metabolism and energetics in chemostats, growth models, competition and predator-prey interactions, as well as the application of rotifer continuous cultures to ecotoxicology and their use in aquaculture are included.