Applied Asymptotic Methods in Nonlinear Oscillations, Yuri A. Mitropolsky; Nguyen Van Dao

Автор: Yuri A. Mitropolsky; Nguyen Van Dao
Название: Applied Asymptotic Methods in Nonlinear Oscillations
ISBN: 079234605X ISBN-13(EAN): 9780792346050
Издательство: Springer
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Цена: 204040.00 T
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Описание: Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations.

Автор: Johan Grasman
Название: Asymptotic Methods for Relaxation Oscillations and Applications
ISBN: 0387965130 ISBN-13(EAN): 9780387965130
Издательство: Springer
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Цена: 87070.00 T
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Описание: 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.

Автор: Elena V. Grigorieva; Sergey A. Kaschenko
Название: Asymptotic Representation of Relaxation Oscillations in Lasers
ISBN: 3319428594 ISBN-13(EAN): 9783319428598
Издательство: Springer
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Цена: 102480.00 T
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Описание: 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.

Автор: Guckenheimer John, Holmes Philip
Название: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
ISBN: 0387908196 ISBN-13(EAN): 9780387908199
Издательство: Springer
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Цена: 121110.00 T
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Описание: From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2

Автор: Mickens Ronald E
Название: Truly Nonlinear Oscillations: Harmonic Balance, Parameter Expansions, Iteration, And Averaging Methods
ISBN: 981429165X ISBN-13(EAN): 9789814291651
Издательство: World Scientific Publishing
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Цена: 100320.00 T
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Описание: Provides a presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of truly nonlinear (TNL) oscillator equations. This volume gives a general overview of the author`s work on harmonic balance, iteration and combined linearization-averaging methods.

Автор: Kabanov Yuri, Pergamenshchikov Sergei
Название: Two-Scale Stochastic Systems / Asymptotic Analysis and Control
ISBN: 3540653325 ISBN-13(EAN): 9783540653325
Издательство: Springer
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Цена: 93160.00 T
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Описание: Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.

Название: Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
ISBN: 3319520415 ISBN-13(EAN): 9783319520414
Издательство: Springer
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Цена: 102480.00 T
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Описание: The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015.

Автор: Alexander Fidlin
Название: Nonlinear Oscillations in Mechanical Engineering
ISBN: 3642066348 ISBN-13(EAN): 9783642066344
Издательство: Springer
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Цена: 113180.00 T
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Описание: Since the nonlinearities are caused, first of all, by contacts between different mechanical parts, the main part of this book is devoted to oscillations in mechanical systems with discontinuities caused by dry friction and collisions.

Автор: Vladimir Fridman; Eugene Sviyazheninov
Название: Theory of Elastic Oscillations
ISBN: 9811047855 ISBN-13(EAN): 9789811047855
Издательство: Springer
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Цена: 139750.00 T
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Описание:

This book presents in detail an alternative approach to solving problems involving both linear and nonlinear oscillations of elastic distributed parameter systems. It includes the so-called variational, projection and iterative gradient methods, which, when applied to nonlinear problems, use the procedure of linearization of the original non-linear equations.

These methods are not universal and require a different solution for each problem or class of problems.However, in many cases the combination of the methods shown in this book leads to more efficient algorithms for solving important applied problems.To record these algorithms in a unified form, the first part of the book and its appendix devote considerable attention to compiling the general operator equations, which include (as particular cases) equations for vibrations in rods, plates, shells and three-dimensional bodies. They are mainly considered to be periodic or nearly periodic oscillations, which correspond to stationary or nearly stationary regimes of machinery operation. In turn, the second part of the book presents a number of solutions for selected applications.

Автор: Jeffrey Rauch; Michael Taylor
Название: Singularities and Oscillations
ISBN: 0387982000 ISBN-13(EAN): 9780387982007
Издательство: Springer
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Цена: 139750.00 T
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Описание: This volume contains a multiplicity of approaches brought to bear on problems varying from the formation of caustics and the propagation of waves at a boundary, to the examination of viscous boundary layers.

Автор: K. Gopalsamy
Название: Stability and Oscillations in Delay Differential Equations of Population Dynamics
ISBN: 0792315944 ISBN-13(EAN): 9780792315940
Издательство: Springer
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Цена: 121110.00 T
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Описание: An overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics covered include linear and nonlinear delay and integrodifferential equations, which have potential applications in biological and physical dynamic processes.

Автор: Hayashi Chihiro
Название: Nonlinear Oscillations in Physical Systems
ISBN: 0691611203 ISBN-13(EAN): 9780691611204
Издательство: Wiley
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Цена: 79200.00 T
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Описание: This book offers a fundamental explanation of nonlinear oscillations in physical systems. Originally intended for electrical engineers, it remains an important reference for the increasing numbers of researchers studying nonlinear phenomena in physics, chemical engineering, biology, medicine, and other fields. Originally published in 1986. The Pr