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Author: A. A. Andronov
Publisher: Elsevier
ISBN: 1483194728
Category : Science
Languages : en
Pages : 848
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Book Description
Theory of Oscillators presents the applications and exposition of the qualitative theory of differential equations. This book discusses the idea of a discontinuous transition in a dynamic process. Organized into 11 chapters, this book begins with an overview of the simplest type of oscillatory system in which the motion is described by a linear differential equation. This text then examines the character of the motion of the representative point along the hyperbola. Other chapters consider examples of two basic types of non-linear non-conservative systems, namely, dissipative systems and self-oscillating systems. This book discusses as well the discontinuous self-oscillations of a symmetrical multi-vibrator neglecting anode reaction. The final chapter deals with the immense practical importance of the stability of physical systems containing energy sources particularly control systems. This book is a valuable resource for electrical engineers, scientists, physicists, and mathematicians.
Author: A. A. Andronov
Publisher: Elsevier
ISBN: 1483194728
Category : Science
Languages : en
Pages : 848
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Book Description
Theory of Oscillators presents the applications and exposition of the qualitative theory of differential equations. This book discusses the idea of a discontinuous transition in a dynamic process. Organized into 11 chapters, this book begins with an overview of the simplest type of oscillatory system in which the motion is described by a linear differential equation. This text then examines the character of the motion of the representative point along the hyperbola. Other chapters consider examples of two basic types of non-linear non-conservative systems, namely, dissipative systems and self-oscillating systems. This book discusses as well the discontinuous self-oscillations of a symmetrical multi-vibrator neglecting anode reaction. The final chapter deals with the immense practical importance of the stability of physical systems containing energy sources particularly control systems. This book is a valuable resource for electrical engineers, scientists, physicists, and mathematicians.
Author: G.A. Leonov
Publisher: Springer Science & Business Media
ISBN: 9400901933
Category : Mathematics
Languages : en
Pages : 415
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Book Description
This book is devoted to nonlocal theory of nonlinear oscillations. The frequency methods of investigating problems of cycle existence in multidimensional analogues of Van der Pol equation, in dynamical systems with cylindrical phase space and dynamical systems satisfying Routh-Hurwitz generalized conditions are systematically presented here for the first time. To solve these problems methods of Poincaré map construction, frequency methods, synthesis of Lyapunov direct methods and bifurcation theory elements are applied. V.M. Popov's method is employed for obtaining frequency criteria, which estimate period of oscillations. Also, an approach to investigate the stability of cycles based on the ideas of Zhukovsky, Borg, Hartmann, and Olech is presented, and the effects appearing when bounded trajectories are unstable are discussed. For chaotic oscillations theorems on localizations of attractors are given. The upper estimates of Hausdorff measure and dimension of attractors generalizing Doudy-Oesterle and Smith theorems are obtained, illustrated by the example of a Lorenz system and its different generalizations. The analytical apparatus developed in the book is applied to the analysis of oscillation of various control systems, pendulum-like systems and those of synchronization. Audience: This volume will be of interest to those whose work involves Fourier analysis, global analysis, and analysis on manifolds, as well as mathematics of physics and mechanics in general. A background in linear algebra and differential equations is assumed.
Author: R.P. Agarwal
Publisher: Springer Science & Business Media
ISBN: 9401594015
Category : Mathematics
Languages : en
Pages : 344
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Book Description
This monograph is devoted to a rapidly developing area of research of the qualitative theory of difference and functional differential equations. In fact, in the last 25 years Oscillation Theory of difference and functional differential equations has attracted many researchers. This has resulted in hundreds of research papers in every major mathematical journal, and several books. In the first chapter of this monograph, we address oscillation of solutions to difference equations of various types. Here we also offer several new fundamental concepts such as oscillation around a point, oscillation around a sequence, regular oscillation, periodic oscillation, point-wise oscillation of several orthogonal polynomials, global oscillation of sequences of real valued functions, oscillation in ordered sets, (!, R, ~)-oscillate, oscillation in linear spaces, oscillation in Archimedean spaces, and oscillation across a family. These concepts are explained through examples and supported by interesting results. In the second chapter we present recent results pertaining to the oscil lation of n-th order functional differential equations with deviating argu ments, and functional differential equations of neutral type. We mainly deal with integral criteria for oscillation. While several results of this chapter were originally formulated for more complicated and/or more general differ ential equations, we discuss here a simplified version to elucidate the main ideas of the oscillation theory of functional differential equations. Further, from a large number of theorems presented in this chapter we have selected the proofs of only those results which we thought would best illustrate the various strategies and ideas involved.
Author: Ravi P. Agarwal
Publisher: Hindawi Publishing Corporation
ISBN: 9775945194
Category : Difference Equations
Languages : en
Pages : 977
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Book Description
This book is devoted to a rapidly developing branch of the qualitative theory of difference equations with or without delays. It presents the theory of oscillation of difference equations, exhibiting classical as well as very recent results in that area. While there are several books on difference equations and also on oscillation theory for ordinary differential equations, there is until now no book devoted solely to oscillation theory for difference equations. This book is filling the gap, and it can easily be used as an encyclopedia and reference tool for discrete oscillation theory. In nine chapters, the book covers a wide range of subjects, including oscillation theory for second-order linear difference equations, systems of difference equations, half-linear difference equations, nonlinear difference equations, neutral difference equations, delay difference equations, and differential equations with piecewise constant arguments. This book summarizes almost 300 recent research papers and hence covers all aspects of discrete oscillation theory that have been discussed in recent journal articles. The presented theory is illustrated with 121 examples throughout the book. Each chapter concludes with a section that is devoted to notes and bibliographical and historical remarks. The book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists. Besides serving as a reference tool for researchers in difference equations, this book can also be easily used as a textbook for undergraduate or graduate classes. It is written at a level easy to understand for college students who have had courses in calculus.
Author: Lynn Erbe
Publisher: Routledge
ISBN: 135142632X
Category : Mathematics
Languages : en
Pages : 504
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Book Description
Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. The book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.
Author: Aleksandr Aleksandrovich Andronov
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 376
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Book Description
Author: Jack K. Hale
Publisher: Courier Dover Publications
ISBN: 0486803260
Category : Mathematics
Languages : en
Pages : 192
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Book Description
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction provides a unified approach for obtaining periodic solutions to nonautonomous and autonomous differential equations. 1963 edition.
Author:
Publisher:
ISBN:
Category : Oscillations
Languages : en
Pages : 358
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Book Description
Author: P.S Landa
Publisher: Springer Science & Business Media
ISBN: 9401587639
Category : Mathematics
Languages : en
Pages : 550
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Book Description
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.
Author: Aleksandr Aleksandrovič Andronov
Publisher:
ISBN:
Category :
Languages : en
Pages : 358
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Book Description
