Biological Oscillators Their Mathematical Analysis

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Biological Oscillators: Their Mathematical Analysis

Author : Theodosios Pavlidis
Publisher : Elsevier
ISBN 13 : 0323159826
Total Pages : 222 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Biological Oscillators: Their Mathematical Analysis by : Theodosios Pavlidis

Download or read book Biological Oscillators: Their Mathematical Analysis written by Theodosios Pavlidis and published by Elsevier. This book was released on 2012-12-02 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biological Oscillators: Their Mathematical Analysis introduces the main features of the dynamic properties of biological oscillators and the mathematical techniques necessary for their investigation. It is not a comprehensive description of all known biological oscillators, since this would require a much bigger volume as well as a different type of expertise. Instead certain classes of biological oscillators are described, and then only in as much detail as required for the study of their dynamics. The opening chapter reviews fundamental mathematical concepts and techniques which will be used in the remainder of the book. These include phase plane techniques; asymptotic techniques of Krylov, Bogoliubov, and Mitopolski; and the describing function. Subsequent chapters discuss examples of biological oscillators; phase shifts and phase response curves; the entrainment of oscillators by external inputs; the dynamics of circadian oscillators; effects of changing environment on the dynamics of biological oscillators; the features peculiar to populations of interacting oscillators; and biological phenomena attributable to populations of oscillators.

Mathematical Models in Molecular Cellular Biology

Author : Lee A. Segel
Publisher : CUP Archive
ISBN 13 : 9780521229258
Total Pages : 776 pages
Book Rating : 4.2/5 (292 download)

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Book Synopsis Mathematical Models in Molecular Cellular Biology by : Lee A. Segel

Download or read book Mathematical Models in Molecular Cellular Biology written by Lee A. Segel and published by CUP Archive. This book was released on 1980 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in theoretical biology is rapidly growing and this 1981 book attempts to make the theory more accessible to experimentalists. Its primary purpose is to demonstrate to experimental molecular and cellular biologists the possible usefulness of mathematical models. Biologists with a basic command of calculus should be able to learn from the book what assumptions are implied by various types of equations, to understand in broad outline a number of major theoretical concepts, and to be aware of some of the difficulties connected with analytical and numerical solutions of mathematical problems. Thus they should be able to appreciate the significance of theoretical papers in their fields and to communicate usefully with theoreticians in the course of their work.

Physics of Biological Oscillators

Author : Aneta Stefanovska
Publisher : Springer Nature
ISBN 13 : 3030598055
Total Pages : 431 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Physics of Biological Oscillators by : Aneta Stefanovska

Download or read book Physics of Biological Oscillators written by Aneta Stefanovska and published by Springer Nature. This book was released on 2021-05-05 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, based on a selection of invited presentations from a topical workshop, focusses on time-variable oscillations and their interactions. The problem is challenging, because the origin of the time variability is usually unknown. In mathematical terms, the oscillations are non-autonomous, reflecting the physics of open systems where the function of each oscillator is affected by its environment. Time-frequency analysis being essential, recent advances in this area, including wavelet phase coherence analysis and nonlinear mode decomposition, are discussed. Some applications to biology and physiology are described. Although the most important manifestation of time-variable oscillations is arguably in biology, they also crop up in, e.g. astrophysics, or for electrons on superfluid helium. The book brings together the research of the best international experts in seemingly very different disciplinary areas.

Oscillations in Mathematical Biology

Author : J.P.E. Hodgson
Publisher : Springer Science & Business Media
ISBN 13 : 3642464807
Total Pages : 205 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Oscillations in Mathematical Biology by : J.P.E. Hodgson

Download or read book Oscillations in Mathematical Biology written by J.P.E. Hodgson and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume are based on talks given at a one day conference held on the campus of Adelphi University in April 1982. The conference was organized with the title "Oscillations in Mathematical Biology;" however the speakers were allowed considerable latitutde in their choice of topics. In the event, the talks all concerned the dynamics of non-linear systems arising in biology so that the conference achieved a good measure of cohesion. Some of the speakers cho~e not to submit a manuscript for these proceedings, feeling that their material was too conjectural to be committed to print. Also the paper of Rinzel and Troy is a distillation of the two separate talks that the authors gave. Otherwise the material reproduces the conference proceedings. The conference was made possible by the generous support of the Office of the Dean of the College of Arts and Sciences at Adelphi. The bulk of the organization of the conference was carried out by Dr. Ronald Grisell whose energy was in large measure responsible for the success of the conference.

Biological Clocks, Rhythms, and Oscillations

Author : Daniel B. Forger
Publisher : MIT Press
ISBN 13 : 0262036770
Total Pages : 369 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Biological Clocks, Rhythms, and Oscillations by : Daniel B. Forger

Download or read book Biological Clocks, Rhythms, and Oscillations written by Daniel B. Forger and published by MIT Press. This book was released on 2017-11-16 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.

Physics of Biological Oscillators

Author : Aneta Stefanovska
Publisher :
ISBN 13 : 9783030598068
Total Pages : 0 pages
Book Rating : 4.5/5 (98 download)

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Book Synopsis Physics of Biological Oscillators by : Aneta Stefanovska

Download or read book Physics of Biological Oscillators written by Aneta Stefanovska and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, based on a selection of invited presentations from a topical workshop, focusses on time-variable oscillations and their interactions. The problem is challenging, because the origin of the time variability is usually unknown. In mathematical terms, the oscillations are non-autonomous, reflecting the physics of open systems where the function of each oscillator is affected by its environment. Time-frequency analysis being essential, recent advances in this area, including wavelet phase coherence analysis and nonlinear mode decomposition, are discussed. Some applications to biology and physiology are described. Although the most important manifestation of time-variable oscillations is arguably in biology, they also crop up in, e.g. astrophysics, or for electrons on superfluid helium. The book brings together the research of the best international experts in seemingly very different disciplinary areas. .

The Geometry of Biological Time

Author : Arthur T. Winfree
Publisher : Springer Science & Business Media
ISBN 13 : 3662224925
Total Pages : 543 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis The Geometry of Biological Time by : Arthur T. Winfree

Download or read book The Geometry of Biological Time written by Arthur T. Winfree and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: As 1 review these pages, the last of them written in Summer 1978, some retrospec tive thoughts come to mind which put the whole business into better perspective for me and might aid the prospective reader in choosing how to approach this volume. The most conspicuous thought in my mind at present is the diversity of wholly independent explorations that came upon phase singularities, in one guise or another, during the past decade. My efforts to gather the published literature during the last phases of actually writing a whole book about them were almost equally divided between libraries of Biology, Chemistry, Engineering, Mathematics, Medicine, and Physics. A lot of what 1 call "gathering " was done somewhat in anticipation in the form of cönjecture, query, and prediction based on analogy between developments in different fields. The consequence throughout 1979 was that our long-suffering publisher re peatedly had to replace such material by citation of unexpected flurries of papers giving substantive demonstration. 1 trust that the authors of these many excellent reports, and especially of those I only found too late, will forgive the brevity of allusion I feIt compelled to observe in these substitutions. A residue of loose ends is largely collected in the index under "QUERIES. " It is c1ear to me already that the materials I began to gather several years ago represented only the first flickering of what turns out to be a substantial conflagration.

Biological Clocks, Rhythms, and Oscillations

Author : Daniel B. Forger
Publisher : MIT Press
ISBN 13 : 0262342359
Total Pages : 368 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Biological Clocks, Rhythms, and Oscillations by : Daniel B. Forger

Download or read book Biological Clocks, Rhythms, and Oscillations written by Daniel B. Forger and published by MIT Press. This book was released on 2017-11-16 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.

Biological Rhythms

Author : Jurgen Aschoff
Publisher : Springer Science & Business Media
ISBN 13 : 1461565529
Total Pages : 565 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Biological Rhythms by : Jurgen Aschoff

Download or read book Biological Rhythms written by Jurgen Aschoff and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in biological rhythms has been traced back more than 2,500]ears to Archilochus, the Greek poet, who in one of his fragments suggests ",,(i,,(VWO'KE o'olos pv{}J.tos txv{}pW7rOVS ~XH" (recognize what rhythm governs man) (Aschoff, 1974). Reference can also be made to the French student of medicine J. J. Virey who, in his thesis of 1814, used for the first time the expression "horloge vivante" (living clock) to describe daily rhythms and to D. C. W. Hufeland (1779) who called the 24-hour period the unit of our natural chronology. However, it was not until the 1930s that real progress was made in the analysis of biological rhythms; and Erwin Bunning was encouraged to publish the first, and still not outdated, monograph in the field in 1958. Two years later, in the middle of exciting discoveries, we took a breather at the Cold Spring Harbor Symposium on Biological Clocks. Its survey on rules considered valid at that time, and Pittendrigh's anticipating view on the temporal organization of living systems, made it a milestone on our way from a more formalistic description of biological rhythms to the understanding of their structural and physiological basis.

Mathematical Models and Their Analysis

Author : Frederick Y. M. Wan
Publisher : SIAM
ISBN 13 : 1611975263
Total Pages : 404 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Mathematical Models and Their Analysis by : Frederick Y. M. Wan

Download or read book Mathematical Models and Their Analysis written by Frederick Y. M. Wan and published by SIAM. This book was released on 2018-03-20 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A great deal can be learned through modeling and mathematical analysis about real-life phenomena, even before numerical simulations are used to accurately portray the specific configuration of a situation. Scientific computing also becomes more effective and efficient if it is preceded by some preliminary analysis. These important advantages of mathematical modeling are demonstrated by models of historical importance in an easily understandable way. The organization of Mathematical Models and Their Analysis groups models by the issues that need to be addressed about the phenomena. The new approach shows how mathematics effective for one modeled phenomenon can be used to analyze another unrelated problem. For instance, the mathematics of differential equations useful in understanding the classical physics of planetary models, fluid motion, and heat conduction is also applicable to the seemingly unrelated phenomena of traffic flow and congestion, offshore sovereignty, and regulation of overfishing and deforestation. The formulation and in-depth analysis of these and other models on modern social issues, such as the management of exhaustible and renewable resources in response to consumption demands and economic growth, are of increasing concern to students and researchers of our time. The modeling of current social issues typically starts with a simple but meaningful model that may not capture all the important elements of the phenomenon. Predictions extracted from such a model may be informative but not compatible with all known observations; so the model may require improvements. The cycle of model formulation, analysis, interpretation, and assessment is made explicit for the modeler to repeat until a model is validated by consistency with all known facts.

Math and Bio 2010

Author : Lynn Arthur Steen
Publisher : MAA
ISBN 13 : 9780883858189
Total Pages : 182 pages
Book Rating : 4.8/5 (581 download)

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Book Synopsis Math and Bio 2010 by : Lynn Arthur Steen

Download or read book Math and Bio 2010 written by Lynn Arthur Steen and published by MAA. This book was released on 2005 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Math and bio 2010 grew out of 'Meeting the Challenges: Education across the Biological, Mathematical and Computer Sciences,' a joint project of the Mathematical Association of America (MAA), the National Science Foundation Division of Undergraduate Education (NSF DUE), the National Institute of General Medical Sciences (NIGMS), the American Association for the Advancement of Science (AAAS), and the American Society for Microbiology (ASM)."--Foreword, p. vi

Nonlinear Dynamics: The Richard Rand 50th Anniversary Volume

Author : Ardeshir Guran
Publisher : World Scientific
ISBN 13 : 981450078X
Total Pages : 248 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Nonlinear Dynamics: The Richard Rand 50th Anniversary Volume by : Ardeshir Guran

Download or read book Nonlinear Dynamics: The Richard Rand 50th Anniversary Volume written by Ardeshir Guran and published by World Scientific. This book was released on 1997-12-16 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers on the subject of nonlinear dynamics and its applications written by experts in this field. It offers the reader a sampling of exciting research areas in this fast-growing field. The topics covered include chaos, tools to analyze motions, fractal boundaries, dynamics of the Fitzhugh-Nagumo equation, structural control, separation of contaminations from signal of interest, parametric excitation, stochastic bifurcation, mode localization in repetitive structures, Toda lattice, transition from soliton to chaotic motion, nonlinear normal modes, noise perturbations of nonlinear dynamical systems, and phase locking of coupled limit cycle oscillators. Mathematical methods include Lie transforms, Monte Carlo simulations, stochastic calculus, perturbation methods and proper orthogonal decomposition. Applications include gyrodynamics, tether connected satellites, shell buckling, nonlinear circuits, volume oscillations of a large lake, systems with stick-slip friction, imperfect or disordered structures, overturning of rigid blocks, central pattern generators, flow induced oscillations, shape control and vibration suppression of elastic structures.All of these diverse contributions have a common thread: the world of nonlinear behavior. Although linear dynamics is an invaluable tool, there are many problems where nonlinear effects are essential. Some examples include bifurcation of solutions, stability of motion, the effects of large displacements, and subharmonic resonance. This book shows how nonlinear dynamics is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.

Biological Clocks

Author : Susan Binkley
Publisher : CRC Press
ISBN 13 : 100015968X
Total Pages : 240 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Biological Clocks by : Susan Binkley

Download or read book Biological Clocks written by Susan Binkley and published by CRC Press. This book was released on 2020-08-26 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biological Clocks introduces the subject of human chronobiology. It describes biological clocks; why we have clocks; how biological clocks relate to sleep disorders, depression, and jet lag; and how the reader can measure his/her own rhythms.

Cellular and Molecular Bases of Biological Clocks

Author : Leland N. Jr. Edmunds
Publisher : Springer Science & Business Media
ISBN 13 : 1461237424
Total Pages : 513 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Cellular and Molecular Bases of Biological Clocks by : Leland N. Jr. Edmunds

Download or read book Cellular and Molecular Bases of Biological Clocks written by Leland N. Jr. Edmunds and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: An intriguing class of biological periodicity consists of rhythms with about 24-hour periods occurring at every level of eukaryotic organization. Progress is being made in understanding these rhythms. The six chapters of this work include a brief introduction to circadian (24-hour) rhythms, a survey of circadian organization at the cellular level, and a description of the important microorganisms that have served as experimental models for biochemical analysis. Also considered are relations between cell division cycles and circadian oscillators, as well as some general and theoretical aspects. Where appropriate, parallels are drawn to neuronal oscillators. This volume will introduce and critically appraise modern chronobiology; its extensive illustrations and comprehensive up-to-date bibliography will make it an authoritative reference.

nonlinear analysis and applications

Author : Lakshmikantham
Publisher : CRC Press
ISBN 13 : 1000147037
Total Pages : 678 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis nonlinear analysis and applications by : Lakshmikantham

Download or read book nonlinear analysis and applications written by Lakshmikantham and published by CRC Press. This book was released on 2020-11-26 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book attempts to put together the works of a wide range of mathematical scientists. It consists of the proceedings of the Seventh Conference on "Nonlinear Analysis and Applications" including papers that were delivered as invited talks and research reports.

A Chaotic Hierarchy

Author : Gerold Baier
Publisher : World Scientific
ISBN 13 : 981461890X
Total Pages : 412 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis A Chaotic Hierarchy by : Gerold Baier

Download or read book A Chaotic Hierarchy written by Gerold Baier and published by World Scientific. This book was released on 1991-03-29 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles introduces the idea of a hierarchical order in chaotic systems and natural phenomena. To understand nature, nonlinear sciences use a multidisciplinary perspective. Therefore the book integrates research work of different fields: experimental evidence for the theory drawn from physics, biology and chemistry; theoretical progress in mathematical treatment, numerical techniques and graphical methods of nonlinear sciences; and to not-yet-understood philosophical and fundamental problems related to chaos and cosmos, chaos and quantum mechanics or evolutionary dynamics. Featuring the most recent advances in nonlinear dynamics this collection should provide an indispensable reference source and starting point for further research concerning dynamical and hierarchical chaotic systems. Besides this book is in honor of Professor O E Rössler, one of the pioneers of Chaos Theory, who celebrated his 50th birthday in May 1990. Contents:Hierarchies of Dynamical Systems (M Klein & G Baier)The Chaotic Hierarchy (O E Rössler)Phase Regulation of Coupled Oscillators and Chaos (R H Abraham)Symbolic Dynamics in the Belousov-Zhabotinskii Reaction: From Rössler's Intuition to Experimental Evidence for Shil'nikov's Homoclinic Chaos (F Argoul et al.)Determinism in a World of Non-Invertible Transformations (H Degn)Structural, Functional and Dynamical Hierarchies in Neural Networks (A V Holden)Climbing Up Dynamical Hierarchy (K Kaneko)Chaotic Hierarchy from the One-Dimensional Box-Within-a-Box Bifurcations Structure Properties (Ch Mira)The Peroxidase-Oxidase Reaction: A Case for Chaos in the Biochemistry of the Cell (L F Olsen et al.)Experimental Progress on the Ladder Towards Higher Chaos (J Peinke et al.)Conjugate Pair of Representations in Chaos and Quantum Mechanics (K Tomita) Readership: Mathematicians, mathematical physicists and condensed matter physicists. Keywords:Nonlinear Dynamics;Chaos;Hyperchaos;Dynamic Hierarchies;Ordinary Differential Equations;Bifurcations

U.S. Environmental Protection Agency Library System Book Catalog

Author : United States. Environmental Protection Agency. Library Systems Branch
Publisher :
ISBN 13 :
Total Pages : 490 pages
Book Rating : 4.:/5 (3 download)

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Book Synopsis U.S. Environmental Protection Agency Library System Book Catalog by : United States. Environmental Protection Agency. Library Systems Branch

Download or read book U.S. Environmental Protection Agency Library System Book Catalog written by United States. Environmental Protection Agency. Library Systems Branch and published by . This book was released on 1975 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: