Applied Asymptotic Methods in Nonlinear Oscillations, Yuri A. Mitropolsky; Nguyen Van Dao
Автор: Elena V. Grigorieva; Sergey A. Kaschenko Название: Asymptotic Representation of Relaxation Oscillations in Lasers ISBN: 3319428594 ISBN-13(EAN): 9783319428598 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
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: Hayashi Chihiro Название: Nonlinear Oscillations in Physical Systems ISBN: 0691611203 ISBN-13(EAN): 9780691611204 Издательство: Wiley Рейтинг: Цена: 11880.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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
Автор: Alexander Fidlin Название: Nonlinear Oscillations in Mechanical Engineering ISBN: 3642066348 ISBN-13(EAN): 9783642066344 Издательство: Springer Рейтинг: Цена: 16977.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Yuri A. Mitropolsky; Nguyen Van Dao Название: Applied Asymptotic Methods in Nonlinear Oscillations ISBN: 9048148650 ISBN-13(EAN): 9789048148653 Издательство: Springer Рейтинг: Цена: 30606.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Tim Van Hoolst; Paul Smeyers Название: Linear Isentropic Oscillations of Stars ISBN: 3642266126 ISBN-13(EAN): 9783642266126 Издательство: Springer Рейтинг: Цена: 26120.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book surveys the theory of free, linear, isentropic oscillations in spherically symmetric, gaseous equilibrium stars, from basic concepts to asymptotic representations of normal modes and with slow period changes in rapidly evolving pulsating stars.
Автор: Vladimir Fridman; Eugene Sviyazheninov Название: Theory of Elastic Oscillations ISBN: 9811047855 ISBN-13(EAN): 9789811047855 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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 Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
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