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Differential Equations With Small Parameters And Relaxation Oscillation
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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 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 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 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 Asymptotic Methods for Relaxation Oscillations and Applications by : Johan Grasman
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.
Book Synopsis Topological Groups by : R. V. Gamkrelidze
Download or read book Topological Groups written by R. V. Gamkrelidze and published by CRC Press. This book was released on 1987-03-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering the insights of L.S. Pontryagin, one of the foremost thinkers in modern mathematics, the second volume in this four-volume set examines the nature and processes that make up topological groups. Already hailed as the leading work in this subject for its abundance of examples and its thorough explanations, the text is arranged so that readers can follow the material either sequentially or schematically. Stand-alone chapters cover such topics as topological division rings, linear representations of compact topological groups, and the concept of a lie group.
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 Multiple Time Scale Dynamics by : Christian Kuehn
Download or read book Multiple Time Scale Dynamics written by Christian Kuehn and published by Springer. This book was released on 2015-02-25 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Book Synopsis Complex Analysis and Dynamical Systems VI by : Matania Ben-Artzi
Download or read book Complex Analysis and Dynamical Systems VI written by Matania Ben-Artzi and published by American Mathematical Soc.. This book was released on 2015-12-03 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19-24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers in this volume range over a wide variety of topics in Partial Differential Equations, Differential Geometry, and the Radon Transform. Taken together, the articles collected here provide the reader with a panorama of activity in partial differential equations and general relativity, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 667) is devoted to complex analysis, quasiconformal mappings, and complex dynamics. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).
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 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 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 Recent Trends in Dynamical Systems by : Andreas Johann
Download or read book Recent Trends in Dynamical Systems written by Andreas Johann and published by Springer Science & Business Media. This book was released on 2013-09-24 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation - Geometric mechanics and control theory - Invariant manifolds, attractors and chaos - Fluid mechanics and elasticity - Perturbations and multiscale problems - Hamiltonian dynamics and KAM theory Researchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.
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
Book Synopsis Asymptotic Expansions for Ordinary Differential Equations by : Wolfgang Wasow
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Book Synopsis Oscillatory Evolution Processes by : Igor Gumowski
Download or read book Oscillatory Evolution Processes written by Igor Gumowski and published by Manchester University Press. This book was released on 1989 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Good,No Highlights or Markup,all pages are intact.
