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 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 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 Biological and Biochemical Oscillators written by Britton Chance and published by Academic Press. This book was released on 2014-06-28 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biological and Biochemical Oscillators compiles papers on biochemical and biological oscillators from a theoretical and experimental standpoint. This book discusses the oscillatory behavior, excitability, and propagation phenomena on membranes and membrane-like interfaces; two-dimensional analysis of chemical oscillators; and chemiluminescence in oscillatory oxidation reactions catalyzed. The problems associated with the computer simulation of oscillating systems; mechanism of single-frequency glycolytic oscillations; excitation wave propagation during heart fibrillation; and biochemical cycle of excitation are also elaborated. This compilation likewise covers the physiological rhythms in Saccharomyces cerevisiae populations; integral and indissociable property of eukaryotic gene-action systems; and role of actidione in the temperature jump response of the circadian rhythm in Euglena gracilis. This publication is valuable to biochemists interested in biochemical and biological oscillations.
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 Biological Oscillators written by Theodosios Pavlidis and published by . This book was released on 1973 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Chronobioengineering written by Donald McEachron and published by Morgan & Claypool Publishers. This book was released on 2012 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: And Conclusion for Proposition 2.3Measuring Time's Passing-the Adaptive Function of Interval Timers; Timing is (Almost) Everything; Overall Conclusions; References; The Circle Game: Mathematics, Models, and Rhythms; Introduction to Mathematical Modeling; Linear Models of Oscillators; Nonlinear Models of Oscillators; Modeling Molecular Networks in Cells; Modeling External Perturbations on Biological Oscillators: Synchronization, Entrainment, and Other Effects on Rhythms.
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.
Download or read book Biological and Biochemical Oscillators written by and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Biology II written by James D. Murray and published by Springer Science & Business Media. This book was released on 2011-02-15 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences. It has been extensively updated and extended to cover much of the growth of mathematical biology. From the reviews: ""This book, a classical text in mathematical biology, cleverly combines mathematical tools with subject area sciences."--SHORT BOOK REVIEWS
Download or read book Phase Resetting in Medicine and Biology written by Peter A. Tass and published by Springer Science & Business Media. This book was released on 2007-01-15 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new theoretical approach to phase resetting and stimulation-induced synchronization and desynchronization in a population of oscillators. The author uses stochastic methods from statistical mechanics and applies his theory to models of practical importance in physiology and neuroscience. The book is accessible to readers not familiar with the mathematical formalism. The author also proposes improvements to stimulation techniques as used by neurologists and neurosurgeons in the context of Parkinson's disease and MEG/EEG data analysis.
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.
Download or read book Mathematical Biology written by James D. Murray and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.
Download or read book Cumulated Index Medicus written by and published by . This book was released on 1993 with total page 1608 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Systems Biology of Cell Signaling written by James Ferrell and published by Garland Science. This book was released on 2021-09-28 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we understand the complexity of genes, RNAs, and proteins and the associated regulatory networks? One approach is to look for recurring types of dynamical behavior. Mathematical models prove to be useful, especially models coming from theories of biochemical reactions such as ordinary differential equation models. Clever, careful experiments test these models and their basis in specific theories. This textbook aims to provide advanced students with the tools and insights needed to carry out studies of signal transduction drawing on modeling, theory, and experimentation. Early chapters summarize the basic building blocks of signaling systems: binding/dissociation, synthesis/destruction, and activation/inactivation. Subsequent chapters introduce various basic circuit devices: amplifiers, stabilizers, pulse generators, switches, stochastic spike generators, and oscillators. All chapters consistently use approaches and concepts from chemical kinetics and nonlinear dynamics, including rate-balance analysis, phase plane analysis, nullclines, linear stability analysis, stable nodes, saddles, unstable nodes, stable and unstable spirals, and bifurcations. This textbook seeks to provide quantitatively inclined biologists and biologically inclined physicists with the tools and insights needed to apply modeling and theory to interesting biological processes. Key Features: Full-color illustration program with diagrams to help illuminate the concepts Enables the reader to apply modeling and theory to the biological processes Further Reading for each chapter High-quality figures available for instructors to download
Download or read book Medical Subject Headings written by National Library of Medicine (U.S.) and published by . This book was released on 1997 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
