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Differential Equations With Small Parameters And Relaxation Oscillations
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Book Synopsis Differential Equations with Small Parameters and Relaxation Oscillations by : E. Mishchenko
Download or read book Differential Equations with Small Parameters and Relaxation Oscillations written by E. Mishchenko and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large amount of work has been done on ordinary differ ential equations with small parameters multiplying deriv atives. This book investigates questions related to the asymptotic calculation of relaxation oscillations, which are periodic solutions formed of sections of both sl- and fast-motion parts of phase trajectories. A detailed discussion of solutions of differential equations involving small parameters is given for regions near singular points. The main results examined were obtained by L.S. Pontryagin and the authors. Other works have also been taken into account: A.A. Dorodnitsyn's investigations of Van der Pol's equation, results obtained by N.A. Zheleztsov and L.V. Rodygin concerning relaxation oscillations in electronic devices, and results due to A.N. Tikhonov and A.B. Vasil'eva concerning differential equations with small parameters multiplying certain derivatives. E.F. Mishchenko N. Kh. Rozov v CONTENTS Chapter I. Dependence of Solutions on Small Parameters. Applications of Relaxation Oscillations 1. Smooth Dependence. Poincare's Theorem . 1 2. Dependence of Solutions on a Parameter, on an Infinite Time Interval 3 3. Equations with Small Parameters 4 Multiplying Derivatives 4. Second-Order Systems. Fast and Slow Motion.
Book Synopsis Differential Equations Containing Small Parameter and Relaxation Oscillations by : Evgeniĭ Frolovich Mishchenko
Download or read book Differential Equations Containing Small Parameter and Relaxation Oscillations written by Evgeniĭ Frolovich Mishchenko and published by . This book was released on 1965 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Equations with Small Parameters and Relaxation Oscillation by : Eugenii F. Mishchenko
Download or read book Differential Equations with Small Parameters and Relaxation Oscillation written by Eugenii F. Mishchenko and published by . This book was released on 1980 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Representation of Relaxation Oscillations in Lasers by : Elena V. Grigorieva
Download or read book Asymptotic Representation of Relaxation Oscillations in Lasers written by Elena V. Grigorieva and published by Birkhäuser. This book was released on 2016-11-09 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Book Synopsis Relaxation Oscillations in Mathematical Models of Ecology by : A. I︠U︡ Kolesov
Download or read book Relaxation Oscillations in Mathematical Models of Ecology written by A. I︠U︡ Kolesov and published by American Mathematical Soc.. This book was released on 1995 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents for the first time a systematic exposition of techniques for constructing relaxation oscillations and methods for investigating stability properties of certain classes of systems with delay. The authors bring out some of the distinctive features that have no analogues in relaxation systems of ordinary differential equations. The exposition provides analysis of significant examples from biophysics, mathematical ecology, and quantum physics that elucidate important patterns. Many unsolved problems are posed. The book would appeal to researchers and specialists interested in the theory and applications of relaxation oscillations.
Book Synopsis Dynamical Systems V by : V.I. Arnold
Download or read book Dynamical Systems V written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
Book Synopsis Differential Equations and Applications by :
Download or read book Differential Equations and Applications written by and published by Elsevier. This book was released on 1978-01-01 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Equations and Applications
Author :Christopher K.R.T. Jones Publisher :Springer Science & Business Media ISBN 13 :1461301173 Total Pages :278 pages Book Rating :4.4/5 (613 download)
Book Synopsis Multiple-Time-Scale Dynamical Systems by : Christopher K.R.T. Jones
Download or read book Multiple-Time-Scale Dynamical Systems written by Christopher K.R.T. Jones and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.
Book Synopsis Using the Mathematics Literature by : Kristine K. Fowler
Download or read book Using the Mathematics Literature written by Kristine K. Fowler and published by CRC Press. This book was released on 2004-05-25 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
Book Synopsis Mathematical Aspects of Hodgkin-Huxley Neural Theory by : Jane Cronin
Download or read book Mathematical Aspects of Hodgkin-Huxley Neural Theory written by Jane Cronin and published by Cambridge University Press. This book was released on 1987-08-28 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the study of mathematical models of electrically active cells, which play an essential role in, for example, nerve conduction and cardiac functions. In the book, Dr Cronin synthesizes and reviews this material and provides a detailed discussion of the Hodgkin-Huxley model for nerve conduction, which forms the cornerstone of this body of work.
Book Synopsis Asymptotic Methods in Singularly Perturbed Systems by : E.F. Mishchenko
Download or read book Asymptotic Methods in Singularly Perturbed Systems written by E.F. Mishchenko and published by Springer. This book was released on 1994-09-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many books devoted to ordinary differential equations con taining small parameters (small perturbations). The investigation of the dependence of solutions, in a finite time interval, on regular perturbations (the small parameter regularly appears on the right-hand sides of the equa tions) was carried out by Poincare and was practically completed long ago. However, problems connected with singular perturbations still attract the attention of mathematicians. This is what we understand by a singularly perturbed system: a system of differential equations dependent on a small parameter is said to be singularly perturbed if, as the parameter tends to zero, Cauchy's resolvent operator for the main range of time values and initial conditions from bounded sets (or the Poincare operator) converges, in a suitable topology, to a limit object acting in a space of smaller dimension. In different cases this general idea of a singularly perturbed system becomes specific and leads to numerous important and interesting problems. A certain class of these problems was only recently considered in mono graphic literature. This class includes problems connected with the so-called relaxation oscillations, a phenomenon well known to physicists, mechani cians, chemists, and ecologists. Van der Pol, Andronov, Haag, Dorodnitsyn, Stoker, Zheleztsov and others were the first to study relaxation oscillations. A comprehensive study of this phenomenon is hindered by considerable mathematical difficulties and requires the development of new asymptotic methods in the theory of differential equations. These methods, interesting in themselves, lead to the statement of new mathematical problems.
Book Synopsis Technological Concepts and Mathematical Models in the Evolution of Modern Engineering Systems by : Mario Lucertini
Download or read book Technological Concepts and Mathematical Models in the Evolution of Modern Engineering Systems written by Mario Lucertini and published by Springer Science & Business Media. This book was released on 2003-11-27 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of historical research studies covers the evolution of technology as knowledge, the emergence of an autonomous engineering science in the Industrial Age, the idea of scientific managment of production and operation systems, and the interaction between mathematical models and technological concepts. The book is published with the support of the UNESCO Venice Office - Regional Office for Science & Technology in Europe as an activity of the Project: The evolution of events, concepts and models in engineering systems.
Book Synopsis Noise and Nonlinear Phenomena in Nuclear Systems by : J.L. Munoz-Cobo
Download or read book Noise and Nonlinear Phenomena in Nuclear Systems written by J.L. Munoz-Cobo and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of the meeting was to facilitate and encourage the application of recent developments in the physical and mathematical sciences to the analysis of deterministic and stochastic processes in nuclear engineering. In contrast with the rapid growth (triggered by computer developments) of nonlinear analysis in other branches of the physical sciences, the theoretical analysis of nuclear reactors is still based on linearized models of the neutronics and thermal-hydraulic feedback loop, an approach that ignores some intrinsic nonlinearities of the real system. The subject of noise was added because of the importance of the noise technique in detecting abnormalities associated with perturbations of sufficient amplitude to generate nonlinear processes. Consequently the organizers of the meeting invited a group of leading researchers in the field of noise and nonlinear phenomena in nuclear systems to report on recent advances in their area of research. A selected subgroup of researchers in areas outside the reactor field provided enlightenment on new theoretical developments of immediate relevance to nuclear dynamics theory.
Book Synopsis Analyzing Multiscale Phenomena Using Singular Perturbation Methods by : Jane Cronin
Download or read book Analyzing Multiscale Phenomena Using Singular Perturbation Methods written by Jane Cronin and published by American Mathematical Soc.. This book was released on with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.
Book Synopsis Dynamical System and Chaos by : Rui Dilão
Download or read book Dynamical System and Chaos written by Rui Dilão and published by Springer Nature. This book was released on 2023-04-06 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical systems. Some freedom is used in the more formal aspects, using only proofs when there is an algorithmic advantage or because a result is simple and powerful. The first part is an introductory course on dynamical systems theory. It can be taught at the master's level during one semester, not requiring specialized mathematical training. In the second part, the author describes some applications of the theory of dynamical systems. Topics often appear in modern dynamical systems and complexity theories, such as singular perturbation theory, delayed equations, cellular automata, fractal sets, maps of the complex plane, and stochastic iterations of function systems are briefly explored for advanced students. The author also explores applications in mechanics, electromagnetism, celestial mechanics, nonlinear control theory, and macroeconomy. A set of problems consolidating the knowledge of the different subjects, including more elaborated exercises, are provided for all chapters.
Book Synopsis Nonlinear Oscillations and Waves in Dynamical Systems by : P.S Landa
Download or read book Nonlinear Oscillations and Waves in Dynamical Systems written by P.S Landa and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
Book Synopsis Recent Studies inPerturbation Theory by : Dimo Uzunov
Download or read book Recent Studies inPerturbation Theory written by Dimo Uzunov and published by BoD – Books on Demand. This book was released on 2017-06-14 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains seven chapters written by noted experts and young researchers who present their recent studies of both pure mathematical problems of perturbation theories and application of perturbation methods to the study of the important topic in physics, for example, renormalization group theory and applications to basic models in theoretical physics (Y. Takashi), the quantum gravity and its detection and measurement (F. Bulnes), atom-photon interactions (E. G. Thrapsaniotis), treatment of spectra and radiation characteristics by relativistic perturbation theory (A. V. Glushkov et al), and Green's function theory and some applications (Jing Huang). The pure mathematical issues are related to the problem of generalization of the boundary layer function method for bisingularly perturbed differential equations (K. Alymkulov and D. A. Torsunov) and to the development of new homotopy asymptotic methods and some of their applications (Baojian Hong).
