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.
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.
Download or read book The Chemostat written by Jérôme Harmand and published by John Wiley & Sons. This book was released on 2017-08-07 with total page 244 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.
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 172 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.
Download or read book Differential Equations and Control Theory written by Z. Deng and published by CRC Press. This book was released on 2020-11-25 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the proceedings from the International Conference on Differential Equations and Control Theory, held recently in Wuhan, China. It provides an overview of current developments in a range of topics including dynamical systems, optimal control theory, stochastic control, chaos, fractals, wavelets and ordinary, partial, functional and stochastic differential equations.
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.
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.
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.
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 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to classical and modern mathematical models, methods, and issues in population ecology.
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 205 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.
Download or read book Adaptive Diversification MPB 48 written by Michael Doebeli and published by Princeton University Press. This book was released on 2011-08-21 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Adaptive biological diversification occurs when frequency-dependent selection generates advantages for rare phenotypes and induces a split of an ancestral lineage into multiple descendant lineages. Using adaptive dynamics theory, individual-based simulations, and partial differential equation models, this book illustrates that adaptive diversification due to frequency-dependent ecological interaction is a theoretically ubiquitous phenomenon"--Provided by publisher.
Download or read book Methods in Microbiology written by and published by Academic Press. This book was released on 1970-02-28 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditional methods of cultivation of micro-organisms provide little control over the ever-changing physical and chemical environments to which growing populations are exposed. The need for a variety of highly standardized conditions of growth and the selection of several new parameters to measure growth or cultural progress has been recognized. This volume describes the measurement and control of the physical and chemical factors that affect or indicate microbial activities, usually in homogeneous liquid culture. An introduction to the general principles of chemical and physical measurements and to the automatic recording and control of them is presented. Some chapters focus on the theoretical and practical aspects of techniques of continuous cultivation in the laboratory with indications of its application to research problems.
Download or read book Continuous Cultures Of Cells written by Pete H. Calcott and published by CRC Press. This book was released on 2020-03-10 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present as broad a perspective as possible to the subject matter. In the construction of the chapters, much has been left to the individual contributors. Some chapters have been written essentially up to the minute reviews of an application or use of continuous culture whilst other have used data obtained in the author‘s own laboratory to illustrate the use of continuous culture as a problem-solving tool. Yet others have concentrated on specific topics and cited a few key ways in which continuous culture can be useful. The approach was left solely up to the contributor.
Download or read book Differential Equations and Control Theory written by Z. Deng and published by CRC Press. This book was released on 2020-11-25 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the proceedings from the International Conference on Differential Equations and Control Theory, held recently in Wuhan, China. It provides an overview of current developments in a range of topics including dynamical systems, optimal control theory, stochastic control, chaos, fractals, wavelets and ordinary, partial, functional and stochastic differential equations.
Download or read book Differential Equations with Applications to Biology written by Shigui Ruan and published by American Mathematical Soc.. This book was released on 1999 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathématiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic differential equations and their applications to biology, epidemiology, neurobiology, physiology and other related areas. The 41 papers included in this volume represent the recent work of leading researchers over a wide range of subjects, including bifurcation theory, chaos, stability theory, boundary value problems, persistence theory, neural networks, disease transmission, population dynamics, pattern formation and more. The text would be suitable for a graduate or advanced undergraduate course study in mathematical biology. Features: An overview of current developments in differential equations and mathematical biology. Authoritative contributions from over 60 leading worldwide researchers. Original, refereed contributions.
Download or read book The Theory of Differential Equations written by Walter G. Kelley and published by Springer Science & Business Media. This book was released on 2010-04-15 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with ordinary differential equations. Unlike most textbooks on the subject, this text includes nonstandard topics such as perturbation methods and differential equations and Mathematica. In addition to the nonstandard topics, this text also contains contemporary material in the area as well as its classical topics. This second edition is updated to be compatible with Mathematica, version 7.0. It also provides 81 additional exercises, a new section in Chapter 1 on the generalized logistic equation, an additional theorem in Chapter 2 concerning fundamental matrices, and many more other enhancements to the first edition. This book can be used either for a second course in ordinary differential equations or as an introductory course for well-prepared students. The prerequisites for this book are three semesters of calculus and a course in linear algebra, although the needed concepts from linear algebra are introduced along with examples in the book. An undergraduate course in analysis is needed for the more theoretical subjects covered in the final two chapters.
Download or read book Stochastic Chemical Reaction Systems in Biology written by Hong Qian and published by Springer Nature. This book was released on 2021-10-18 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.
