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.
Download or read book Biological Oscillators written by Theodosios Pavlidis and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Biological Oscillators: Their Mathematical Analysis ...
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.
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.
Download or read book Biological Clocks Rhythms and Oscillations written by Daniel B. Forger and published by MIT Press. This book was released on 2024-08-06 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.
Download or read book Mathematical Analysis of Complex Cellular Activity written by Richard Bertram and published by Springer. This book was released on 2015-10-09 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently. The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes. Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells Review 2: Vivien Kirk, James Sneyd: Nonlinear Dynamics of Calcium
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. .
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 2013-03-09 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dealing with dynamics of processes that repeat themselves regularly, this revised and updated edition extends the thread from 1980 to the present day, concentrating on areas of interest where there will be much activity in the future. This involves going through spatial biochemical, electrophysiological, and organismic dynamical systems and patterns that were discovered by pursuing the theme of phase singularities introduced in the original book. In particular the work on excitability in cell membranes will be thoroughly updated as will the references throughout the book.
Download or read book Oscillation and Stability of Delay Models in Biology written by Ravi P. Agarwal and published by Springer. This book was released on 2014-06-07 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Environmental variation plays an important role in many biological and ecological dynamical systems. This monograph focuses on the study of oscillation and the stability of delay models occurring in biology. The book presents recent research results on the qualitative behavior of mathematical models under different physical and environmental conditions, covering dynamics including the distribution and consumption of food. Researchers in the fields of mathematical modeling, mathematical biology, and population dynamics will be particularly interested in this material.
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.
Download or read book Nonlinear Oscillations in Biology and Chemistry written by Hans G. Othmer and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a meeting entitled 'Nonlinear Oscillations in Biology and Chemistry', which was held at the University of Utah May 9-11,1985. The papers fall into four major categories: (i) those that deal with biological problems, particularly problems arising in cell biology, (ii) those that deal with chemical systems, (iii) those that treat problems which arise in neurophysiology, and (iv), those whose primary emphasis is on more general models and the mathematical techniques involved in their analysis. Except for the paper by Auchmuty, all are based on talks given at the meeting. The diversity of papers gives some indication of the scope of the meeting, but the printed word conveys neither the degree of interaction between the participants nor the intellectual sparks generated by that interaction. The meeting was made possible by the financial support of the Department of Mathe matics of the University of Utah. I am indebted to Ms. Toni Bunker of the Department of Mathematics for her very able assistance on all manner of details associated with the organization of the meeting. Finally, a word of thanks to all participants for their con tributions to the success of the meeting, and to the contributors to this volume for their efforts in preparing their manuscripts.
Download or read book Asymptotic Methods for Relaxation Oscillations and Applications written by Johan Grasman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: In various fields of science, notably in physics and biology, one is con fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.
Download or read book From Clocks to Chaos written by Leon Glass and published by Princeton University Press. This book was released on 2020-11-10 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an important new contribution to the literature of chaos, two distinguished researchers in the field of physiology probe central theoretical questions about physiological rhythms. Topics discussed include: How are rhythms generated? How do they start and stop? What are the effects of perturbation of the rhythms? How are oscillations organized in space? Leon Glass and Michael Mackey address an audience of biological scientists, physicians, physical scientists, and mathematicians, but the work assumes no knowledge of advanced mathematics. Variation of rhythms outside normal limits, or appearance of new rhythms where none existed previously, are associated with disease. One of the most interesting features of the book is that it makes a start at explaining "dynamical diseases" that are not the result of infection by pathogens but that stem from abnormalities in the timing of essential functions. From Clocks to Chaos provides a firm foundation for understanding dynamic processes in physiology.
Download or read book The Mathematical Structure of the Human Sleep Wake Cycle written by Steven H. Strogatz and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past three years I have grown accustomed to the puzzled look which appears on people's faces when they hear that I am a mathematician who studies sleep. They wonder, but are usually too polite to ask, what does mathematics have to do with sleep? Instead they ask the questions that fascinate us all: Why do we have to sleep? How much sleep do we really need? Why do we dream? These questions usually spark a lively discussion leading to the exchange of anecdotes, last night's dreams, and other personal information. But they are questions about the func tion of sleep and, interesting as they are, I shall have little more to say about them here. The questions that have concerned me deal instead with the timing of sleep. For those of us on a regular schedule, questions of timing may seem vacuous. We go to bed at night and get up in the morning, going through a cycle of sleeping and waking every 24 hours. Yet to a large extent, the cycle is imposed by the world around us.
Download or read book National Library of Medicine Current Catalog written by National Library of Medicine (U.S.) and published by . This book was released on 1974 with total page 1242 pages. Available in PDF, EPUB and Kindle. Book excerpt: First multi-year cumulation covers six years: 1965-70.
Download or read book An Introduction to the History of Chronobiology Volume 3 written by Jole Shackelford and published by University of Pittsburgh Press. This book was released on 2022-12-27 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: In three volumes, historian Jole Shackelford delineates the history of the study of biological rhythms—now widely known as chronobiology—from antiquity into the twentieth century. Perhaps the most well-known biological rhythm is the circadian rhythm, tied to the cycles of day and night and often referred to as the “body clock.” But there are many other biological rhythms, and although scientists and the natural philosophers who preceded them have long known about them, only in the past thirty years have a handful of pioneering scientists begun to study such rhythms in plants and animals seriously. Tracing the intellectual and institutional development of biological rhythm studies, Shackelford offers a meaningful, evidence-based account of a field that today holds great promise for applications in agriculture, health care, and public health. Volume 1 follows early biological observations and research, chiefly on plants; volume 2 turns to animal and human rhythms and the disciplinary contexts for chronobiological investigation; and volume 3 focuses primarily on twentieth-century researchers who modeled biological clocks and sought them out, including three molecular biologists whose work in determining clock mechanisms earned them a Nobel Prize in 2017.
Download or read book Introduction to Mathematics for Life Scientists written by Edward Batschelet and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "...Here we have a book which we can wholeheartedly suggest. The mathematics is sound and pared to essentials; the examples are an impressive, well-chosen selection from the biomathematics literature, and the problem sets provide both useful exercises and some fine introductions to the art of modeling... Batschelet has written an introduction to biomathematics which is notable for its clarity - not only a clarity of presentation, but also a clarity of purpose, backed by a sure grasp of the field..." #Bulletin of Mathematical Biology#1 "For research workers in the biomedical field who feel a need for freshening up their knowledge in mathematics, but so far have always been frustrated by either too formal or too boring textbooks, there is now exactly what they would like to have: an easy to read introduction. This book is highly motivating for practical workers because only those mathematical techniques are offered for which there is an application in the life sciences. The reader will find it stimulating that each tool described is immediately exemplified by problems from latest publications." #Int. Zeitschrift für klinische Pharmakologie, Therapie und Toxikologie#2
