Dynamics Of The Chemostat

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Dynamics of the Chemostat

Author : Abdelhamid Ajbar
Publisher : CRC Press
ISBN 13 : 1439867143
Total Pages : 370 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Dynamics of the Chemostat by : Abdelhamid Ajbar

Download or read book Dynamics of the Chemostat written by Abdelhamid Ajbar and published by CRC Press. This book was released on 2011-08-09 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Theory of the Chemostat

Author : Hal L. Smith
Publisher : Cambridge University Press
ISBN 13 : 9780521470278
Total Pages : 334 pages
Book Rating : 4.4/5 (72 download)

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Book Synopsis The Theory of the Chemostat by : Hal L. Smith

Download or read book The Theory of the Chemostat written by Hal L. Smith and published by Cambridge University Press. This book was released on 1995-01-27 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic modelling, analysis and simulation of systems that have proven effective in real ecological applications.

The Chemostat

Author : Jérôme Harmand
Publisher : John Wiley & Sons
ISBN 13 : 1119437121
Total Pages : 246 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis The Chemostat by : Jérôme Harmand

Download or read book The Chemostat written by Jérôme Harmand and published by John Wiley & Sons. This book was released on 2017-07-19 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Dynamics of Bacterial Populations Maintained in the Chemostat

Author : Hermann Moser
Publisher :
ISBN 13 :
Total Pages : 146 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis The Dynamics of Bacterial Populations Maintained in the Chemostat by : Hermann Moser

Download or read book The Dynamics of Bacterial Populations Maintained in the Chemostat written by Hermann Moser and published by . This book was released on 1958 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Plankton Regulation Dynamics

Author : Norbert Walz
Publisher : Springer Science & Business Media
ISBN 13 : 3642778046
Total Pages : 310 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Plankton Regulation Dynamics by : Norbert Walz

Download or read book Plankton Regulation Dynamics written by Norbert Walz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamic Models and Control of Biological Systems

Author : Vadrevu Sree Hari Rao
Publisher : Springer Science & Business Media
ISBN 13 : 1441903593
Total Pages : 279 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Dynamic Models and Control of Biological Systems by : Vadrevu Sree Hari Rao

Download or read book Dynamic Models and Control of Biological Systems written by Vadrevu Sree Hari Rao and published by Springer Science & Business Media. This book was released on 2009-07-30 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Biology has grown at an astonishing rate and has established itself as a distinct discipline. Mathematical modeling is now being applied in every major discipline in the biological sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems which arise in the biological sciences and gives some indication of the wide spectrum of questions that modeling can address.

Dynamic Energy Budget Theory for Metabolic Organisation

Author : S. A. L. M. Kooijman
Publisher : Cambridge University Press
ISBN 13 : 052113191X
Total Pages : 533 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis Dynamic Energy Budget Theory for Metabolic Organisation by : S. A. L. M. Kooijman

Download or read book Dynamic Energy Budget Theory for Metabolic Organisation written by S. A. L. M. Kooijman and published by Cambridge University Press. This book was released on 2010 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dynamic Energy Budget theory unifies the commonalities between organisms and links different levels of biological organisation.

Partial Differential Equations in Ecology

Author : Sergei Petrovski
Publisher : MDPI
ISBN 13 : 3036502963
Total Pages : 238 pages
Book Rating : 4.0/5 (365 download)

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Book Synopsis Partial Differential Equations in Ecology by : Sergei Petrovski

Download or read book Partial Differential Equations in Ecology written by Sergei Petrovski and published by MDPI. This book was released on 2021-03-17 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

Dynamical Systems in Population Biology

Author : Xiao-Qiang Zhao
Publisher : Springer Science & Business Media
ISBN 13 : 0387217614
Total Pages : 285 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Dynamical Systems in Population Biology by : Xiao-Qiang Zhao

Download or read book Dynamical Systems in Population Biology written by Xiao-Qiang Zhao and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Population dynamics is an important subject in mathematical biology. A cen tral problem is to study the long-term behavior of modeling systems. Most of these systems are governed by various evolutionary equations such as difference, ordinary, functional, and partial differential equations (see, e. g. , [165, 142, 218, 119, 55]). As we know, interactive populations often live in a fluctuating environment. For example, physical environmental conditions such as temperature and humidity and the availability of food, water, and other resources usually vary in time with seasonal or daily variations. Therefore, more realistic models should be nonautonomous systems. In particular, if the data in a model are periodic functions of time with commensurate period, a periodic system arises; if these periodic functions have different (minimal) periods, we get an almost periodic system. The existing reference books, from the dynamical systems point of view, mainly focus on autonomous biological systems. The book of Hess [106J is an excellent reference for periodic parabolic boundary value problems with applications to population dynamics. Since the publication of this book there have been extensive investigations on periodic, asymptotically periodic, almost periodic, and even general nonautonomous biological systems, which in turn have motivated further development of the theory of dynamical systems. In order to explain the dynamical systems approach to periodic population problems, let us consider, as an illustration, two species periodic competitive systems dUI dt = !I(t,Ul,U2), (0.

Mathematics for Ecology and Environmental Sciences

Author : Yasuhiro Takeuchi
Publisher : Springer Science & Business Media
ISBN 13 : 3540344284
Total Pages : 189 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Mathematics for Ecology and Environmental Sciences by : Yasuhiro Takeuchi

Download or read book Mathematics for Ecology and Environmental Sciences written by Yasuhiro Takeuchi and published by Springer Science & Business Media. This book was released on 2007-01-19 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume discusses the rich and interesting properties of dynamical systems that appear in ecology and environmental sciences. It provides a fascinating survey of the theory of dynamical systems in ecology and environmental science. Each chapter introduces students and scholars to the state-of-the-art in an exciting area, presents new results, and inspires future contributions to mathematical modeling in ecology and environmental sciences.

Adaptive Diversification

Author : Michael Doebeli
Publisher : Princeton University Press
ISBN 13 : 1400838932
Total Pages : 346 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Adaptive Diversification by : Michael Doebeli

Download or read book Adaptive Diversification written by Michael Doebeli and published by Princeton University Press. This book was released on 2011-08-01 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : N. MacDonald
Publisher : Springer Science & Business Media
ISBN 13 : 3642931073
Total Pages : 122 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Time Lags in Biological Models by : N. MacDonald

Download or read book Time Lags in Biological Models written by N. MacDonald and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Chemical Engineering Dynamics

Author : John Ingham
Publisher : John Wiley & Sons
ISBN 13 : 3527614222
Total Pages : 640 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Chemical Engineering Dynamics by : John Ingham

Download or read book Chemical Engineering Dynamics written by John Ingham and published by John Wiley & Sons. This book was released on 2008-02-08 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the modelling of dynamic chemical engineering processes is presented in a highly understandable way using the unique combination of simplified fundamental theory and direct hands-on computer simulation. The mathematics is kept to a minimum, and yet the nearly 100 examples supplied on www.wiley-vch.de illustrate almost every aspect of chemical engineering science. Each example is described in detail, including the model equations. They are written in the modern user-friendly simulation language Berkeley Madonna, which can be run on both Windows PC and Power-Macintosh computers. Madonna solves models comprising many ordinary differential equations using very simple programming, including arrays. It is so powerful that the model parameters may be defined as "sliders", which allow the effect of their change on the model behavior to be seen almost immediately. Data may be included for curve fitting, and sensitivity or multiple runs may be performed. The results can be seen simultaneously on multiple-graph windows or by using overlays. The resultant learning effect of this is tremendous. The examples can be varied to fit any real situation, and the suggested exercises provide practical guidance. The extensive experience of the authors, both in university teaching and international courses, is reflected in this well-balanced presentation, which is suitable for the teacher, the student, the chemist or the engineer. This book provides a greater understanding of the formulation and use of mass and energy balances for chemical engineering, in a most stimulating manner. This book is a third edition, which also includes biological, environmental and food process examples.

Introduction to Polyphasic Dispersed Systems Theory

Author : Jacques Thierie
Publisher : Springer
ISBN 13 : 3319278533
Total Pages : 210 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Introduction to Polyphasic Dispersed Systems Theory by : Jacques Thierie

Download or read book Introduction to Polyphasic Dispersed Systems Theory written by Jacques Thierie and published by Springer. This book was released on 2015-12-30 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elements of Mathematical Ecology

Author : Mark Kot
Publisher : Cambridge University Press
ISBN 13 : 1316584054
Total Pages : 466 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Elements of Mathematical Ecology by : Mark Kot

Download or read book Elements of Mathematical Ecology written by Mark Kot and published by Cambridge University Press. This book was released on 2001-07-19 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thoughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text.

Introduction to Mathematical Biology

Author : Ching Shan Chou
Publisher : Springer
ISBN 13 : 3319296388
Total Pages : 174 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Introduction to Mathematical Biology by : Ching Shan Chou

Download or read book Introduction to Mathematical Biology written by Ching Shan Chou and published by Springer. This book was released on 2016-04-27 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a one semester course that the authors have been teaching for several years, and includes two sets of case studies. The first includes chemostat models, predator-prey interaction, competition among species, the spread of infectious diseases, and oscillations arising from bifurcations. In developing these topics, readers will also be introduced to the basic theory of ordinary differential equations, and how to work with MATLAB without having any prior programming experience. The second set of case studies were adapted from recent and current research papers to the level of the students. Topics have been selected based on public health interest. This includes the risk of atherosclerosis associated with high cholesterol levels, cancer and immune interactions, cancer therapy, and tuberculosis. Readers will experience how mathematical models and their numerical simulations can provide explanations that guide biological and biomedical research. Considered to be the undergraduate companion to the more advanced book "Mathematical Modeling of Biological Processes" (A. Friedman, C.-Y. Kao, Springer – 2014), this book is geared towards undergraduate students with little background in mathematics and no biological background.

An Introduction to Delay Differential Equations with Applications to the Life Sciences

Author : hal smith
Publisher : Springer Science & Business Media
ISBN 13 : 1441976469
Total Pages : 178 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis An Introduction to Delay Differential Equations with Applications to the Life Sciences by : hal smith

Download or read book An Introduction to Delay Differential Equations with Applications to the Life Sciences written by hal smith and published by Springer Science & Business Media. This book was released on 2010-09-29 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the applications quickly. The author has used preliminary notes in teaching such a course at Arizona State University over the past two years. This book focuses on the key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models involving delay differential equations. The book begins with a survey of mathematical models involving delay equations.