Dynamical Models In Biology

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Dynamical Models in Biology

Miklós Farkas
Dynamical Models in Biology Book PDF

Author : Miklós Farkas
Publisher : Academic Press
Page : 187 pages
File Size : 49,7 Mb
Release : 2001-06-15
Category : Mathematics
ISBN : 0080530605

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Dynamical Models in Biology by Miklós Farkas Pdf

Dynamic Models in Biology offers an introduction to modern mathematical biology. This book provides a short introduction to modern mathematical methods in modeling dynamical phenomena and treats the broad topics of population dynamics, epidemiology, evolution, immunology, morphogenesis, and pattern formation. Primarily employing differential equations, the author presents accessible descriptions of difficult mathematical models. Recent mathematical results are included, but the author's presentation gives intuitive meaning to all the main formulae. Besides mathematicians who want to get acquainted with this relatively new field of applications, this book is useful for physicians, biologists, agricultural engineers, and environmentalists. Key Topics Include: Chaotic dynamics of populations The spread of sexually transmitted diseases Problems of the origin of life Models of immunology Formation of animal hide patterns The intuitive meaning of mathematical formulae explained with many figures Applying new mathematical results in modeling biological phenomena Miklos Farkas is a professor at Budapest University of Technology where he has researched and instructed mathematics for over thirty years. He has taught at universities in the former Soviet Union, Canada, Australia, Venezuela, Nigeria, India, and Columbia. Prof. Farkas received the 1999 Bolyai Award of the Hungarian Academy of Science and the 2001 Albert Szentgyorgyi Award of the Hungarian Ministry of Education. A 'down-to-earth' introduction to the growing field of modern mathematical biology Also includes appendices which provide background material that goes beyond advanced calculus and linear algebra

Dynamic Models in Biology

Stephen P. Ellner,John Guckenheimer
Dynamic Models in Biology Book PDF

Author : Stephen P. Ellner,John Guckenheimer
Publisher : Princeton University Press
Page : 352 pages
File Size : 51,7 Mb
Release : 2011-09-19
Category : Science
ISBN : 9781400840960

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Dynamic Models in Biology by Stephen P. Ellner,John Guckenheimer Pdf

From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering.

Dynamical Models of Biology and Medicine

Yang Kuang,Meng Fan,Shengqiang Liu,Wanbiao Ma
Dynamical Models of Biology and Medicine Book PDF

Author : Yang Kuang,Meng Fan,Shengqiang Liu,Wanbiao Ma
Publisher : MDPI
Page : 292 pages
File Size : 48,9 Mb
Release : 2019-10-04
Category : Technology & Engineering
ISBN : 9783039212170

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Dynamical Models of Biology and Medicine by Yang Kuang,Meng Fan,Shengqiang Liu,Wanbiao Ma Pdf

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicine

Dynamical Systems in Population Biology

Xiao-Qiang Zhao
Dynamical Systems in Population Biology Book PDF

Author : Xiao-Qiang Zhao
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 42,8 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9780387217611

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Dynamical Systems in Population Biology by Xiao-Qiang Zhao Pdf

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.

Dynamic Models and Control of Biological Systems

Vadrevu Sree Hari Rao,Ponnada Raja Sekhara Rao
Dynamic Models and Control of Biological Systems Book PDF

Author : Vadrevu Sree Hari Rao,Ponnada Raja Sekhara Rao
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 53,5 Mb
Release : 2009-07-30
Category : Science
ISBN : 9781441903594

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Dynamic Models and Control of Biological Systems by Vadrevu Sree Hari Rao,Ponnada Raja Sekhara Rao Pdf

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.

Modeling Dynamic Biological Systems

Bruce Hannon,Matthias Ruth
Modeling Dynamic Biological Systems Book PDF

Author : Bruce Hannon,Matthias Ruth
Publisher : Springer
Page : 434 pages
File Size : 47,6 Mb
Release : 2014-07-05
Category : Science
ISBN : 9783319056159

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Modeling Dynamic Biological Systems by Bruce Hannon,Matthias Ruth Pdf

Many biologists and ecologists have developed models that find widespread use in theoretical investigations and in applications to organism behavior, disease control, population and metapopulation theory, ecosystem dynamics, and environmental management. This book captures and extends the process of model development by concentrating on the dynamic aspects of these processes and by providing the tools such that virtually anyone with basic knowledge in the Life Sciences can develop meaningful dynamic models. Examples of the systems modeled in the book range from models of cell development, the beating heart, the growth and spread of insects, spatial competition and extinction, to the spread and control of epidemics, including the conditions for the development of chaos. Key features: - easy-to-learn and easy-to-use software - examples from many subdisciplines of biology, covering models of cells, organisms, populations, and metapopulations - no prior computer or programming experience required Key benefits: - learn how to develop modeling skills and system thinking on your own rather than use models developed by others - be able to easily run models under alternative assumptions and investigate the implications of these assumptions for the dynamics of the biological system being modeled - develop skills to assess the dynamics of biological systems

Stochastic Dynamics for Systems Biology

Christian Mazza,Michel Benaim
Stochastic Dynamics for Systems Biology Book PDF

Author : Christian Mazza,Michel Benaim
Publisher : CRC Press
Page : 274 pages
File Size : 47,7 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781466514942

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Stochastic Dynamics for Systems Biology by Christian Mazza,Michel Benaim Pdf

Stochastic Dynamics for Systems Biology is one of the first books to provide a systematic study of the many stochastic models used in systems biology. The book shows how the mathematical models are used as technical tools for simulating biological processes and how the models lead to conceptual insights on the functioning of the cellular processing

The Dynamics of Biological Systems

Arianna Bianchi,Thomas Hillen,Mark A. Lewis,Yingfei Yi
The Dynamics of Biological Systems Book PDF

Author : Arianna Bianchi,Thomas Hillen,Mark A. Lewis,Yingfei Yi
Publisher : Springer Nature
Page : 267 pages
File Size : 52,7 Mb
Release : 2019-10-02
Category : Mathematics
ISBN : 9783030225834

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The Dynamics of Biological Systems by Arianna Bianchi,Thomas Hillen,Mark A. Lewis,Yingfei Yi Pdf

The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.

Dynamical Models of Biology and Medicine

Meng Fan,Yang Kuang,Shengqiang Liu,Wanbiao Ma
Dynamical Models of Biology and Medicine Book PDF

Author : Meng Fan,Yang Kuang,Shengqiang Liu,Wanbiao Ma
Publisher : Unknown
Page : 1 pages
File Size : 48,9 Mb
Release : 2019
Category : Electronic books
ISBN : 3039212184

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Dynamical Models of Biology and Medicine by Meng Fan,Yang Kuang,Shengqiang Liu,Wanbiao Ma Pdf

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicine.

Dynamical Systems for Biological Modeling

Fred Brauer,Christopher Kribs
Dynamical Systems for Biological Modeling Book PDF

Author : Fred Brauer,Christopher Kribs
Publisher : CRC Press
Page : 482 pages
File Size : 45,6 Mb
Release : 2015-12-23
Category : Mathematics
ISBN : 9781498774048

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Dynamical Systems for Biological Modeling by Fred Brauer,Christopher Kribs Pdf

Dynamical Systems for Biological Modeling: An Introduction prepares both biology and mathematics students with the understanding and techniques necessary to undertake basic modeling of biological systems. It achieves this through the development and analysis of dynamical systems.The approach emphasizes qualitative ideas rather than explicit computa

Applications of Dynamical Systems in Biology and Medicine

Trachette Jackson,Ami Radunskaya
Applications of Dynamical Systems in Biology and Medicine Book PDF

Author : Trachette Jackson,Ami Radunskaya
Publisher : Springer
Page : 233 pages
File Size : 49,7 Mb
Release : 2015-07-06
Category : Mathematics
ISBN : 9781493927821

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Applications of Dynamical Systems in Biology and Medicine by Trachette Jackson,Ami Radunskaya Pdf

This volume highlights problems from a range of biological and medical applications that can be interpreted as questions about system behavior or control. Topics include drug resistance in cancer and malaria, biological fluid dynamics, auto-regulation in the kidney, anti-coagulation therapy, evolutionary diversification and photo-transduction. Mathematical techniques used to describe and investigate these biological and medical problems include ordinary, partial and stochastic differentiation equations, hybrid discrete-continuous approaches, as well as 2 and 3D numerical simulation.

Dynamical Systems and Their Applications in Biology

Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu
Dynamical Systems and Their Applications in Biology Book PDF

Author : Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 49,9 Mb
Release : 2003
Category : Science
ISBN : 9780821831632

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Dynamical Systems and Their Applications in Biology by Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu Pdf

This volume is based on the proceedings of the International Workshop on Dynamical Systems and their Applications in Biology held at the Canadian Coast Guard College on Cape Breton Island (Nova Scotia, Canada). It presents a broad picture of the current research surrounding applications of dynamical systems in biology, particularly in population biology. The book contains 19 papers and includes articles on the qualitative and/or numerical analysis of models involving ordinary, partial, functional, and stochastic differential equations. Applications include epidemiology, population dynamics, and physiology. The material is suitable for graduate students and research mathematicians interested in ordinary differential equations and their applications in biology. Also available by Ruan, Wolkowicz, and Wu is Differential Equations with Applications to Biology, Volume 21 in the AMS series Fields Institute Communications.

Modeling Life

Alan Garfinkel,Jane Shevtsov,Yina Guo
Modeling Life Book PDF

Author : Alan Garfinkel,Jane Shevtsov,Yina Guo
Publisher : Springer
Page : 445 pages
File Size : 47,7 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9783319597317

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Modeling Life by Alan Garfinkel,Jane Shevtsov,Yina Guo Pdf

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?

Dynamic Systems Biology Modeling and Simulation

Joseph DiStefano III
Dynamic Systems Biology Modeling and Simulation Book PDF

Author : Joseph DiStefano III
Publisher : Academic Press
Page : 884 pages
File Size : 55,7 Mb
Release : 2015-01-10
Category : Science
ISBN : 9780124104938

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Dynamic Systems Biology Modeling and Simulation by Joseph DiStefano III Pdf

Dynamic Systems Biology Modeling and Simuation consolidates and unifies classical and contemporary multiscale methodologies for mathematical modeling and computer simulation of dynamic biological systems – from molecular/cellular, organ-system, on up to population levels. The book pedagogy is developed as a well-annotated, systematic tutorial – with clearly spelled-out and unified nomenclature – derived from the author’s own modeling efforts, publications and teaching over half a century. Ambiguities in some concepts and tools are clarified and others are rendered more accessible and practical. The latter include novel qualitative theory and methodologies for recognizing dynamical signatures in data using structural (multicompartmental and network) models and graph theory; and analyzing structural and measurement (data) models for quantification feasibility. The level is basic-to-intermediate, with much emphasis on biomodeling from real biodata, for use in real applications. Introductory coverage of core mathematical concepts such as linear and nonlinear differential and difference equations, Laplace transforms, linear algebra, probability, statistics and stochastics topics; PLUS ....... The pertinent biology, biochemistry, biophysics or pharmacology for modeling are provided, to support understanding the amalgam of “math modeling” with life sciences. Strong emphasis on quantifying as well as building and analyzing biomodels: includes methodology and computational tools for parameter identifiability and sensitivity analysis; parameter estimation from real data; model distinguishability and simplification; and practical bioexperiment design and optimization. Companion website provides solutions and program code for examples and exercises using Matlab, Simulink, VisSim, SimBiology, SAAMII, AMIGO, Copasi and SBML-coded models. A full set of PowerPoint slides are available from the author for teaching from his textbook. He uses them to teach a 10 week quarter upper division course at UCLA, which meets twice a week, so there are 20 lectures. They can easily be augmented or stretched for a 15 week semester course. Importantly, the slides are editable, so they can be readily adapted to a lecturer’s personal style and course content needs. The lectures are based on excerpts from 12 of the first 13 chapters of DSBMS. They are designed to highlight the key course material, as a study guide and structure for students following the full text content. The complete PowerPoint slide package (~25 MB) can be obtained by instructors (or prospective instructors) by emailing the author directly, at: [email protected]

Dynamics of Biological Systems

Michael Small
Dynamics of Biological Systems Book PDF

Author : Michael Small
Publisher : CRC Press
Page : 286 pages
File Size : 47,7 Mb
Release : 2011-08-25
Category : Mathematics
ISBN : 9781439853368

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Dynamics of Biological Systems by Michael Small Pdf

From the spontaneous rapid firing of cortical neurons to the spatial diffusion of disease epidemics, biological systems exhibit rich dynamic behaviour over a vast range of time and space scales. Unifying many of these diverse phenomena, Dynamics of Biological Systems provides the computational and mathematical platform from which to understand the underlying processes of the phenomena. Through an extensive tour of various biological systems, the text introduces computational methods for simulating spatial diffusion processes in excitable media, such as the human heart, as well as mathematical tools for dealing with systems of nonlinear ordinary and partial differential equations, such as neuronal activation and disease diffusion. The mathematical models and computer simulations offer insight into the dynamics of temporal and spatial biological systems, including cardiac pacemakers, artificial electrical defibrillation, pandemics, pattern formation, flocking behaviour, the interaction of autonomous agents, and hierarchical and structured network topologies. Tools from complex systems and complex networks are also presented for dealing with real phenomenological systems. With exercises and projects in each chapter, this classroom-tested text shows students how to apply a variety of mathematical and computational techniques to model and analyze the temporal and spatial phenomena of biological systems. MATLAB® implementations of algorithms and case studies are available on the author’s website.