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
Описание: Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem.This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study.Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior.
Автор: P.G. Bakker Название: Bifurcations in Flow Patterns ISBN: 079231428X ISBN-13(EAN): 9780792314288 Издательство: Springer Рейтинг: Цена: 22203.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Remco I. Leine; Henk Nijmeijer Название: Dynamics and Bifurcations of Non-Smooth Mechanical Systems ISBN: 3642060293 ISBN-13(EAN): 9783642060298 Издательство: Springer Рейтинг: Цена: 21655.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields.
Описание: The investigation of wave packets and their bi- furcations is very interesting, and useful theoretically and in practice, not only in geophysical fluid dynamics, which is the field to which the theory is being applied here, but also in other fields in mathematics and the natural sciences.
Автор: George Exadaktylos; Ioannis G. Vardoulakis Название: Bifurcations, Instabilities, Degradation in Geomechanics ISBN: 3642080448 ISBN-13(EAN): 9783642080449 Издательство: Springer Рейтинг: Цена: 30606.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is an up-to-date review of developments in the field of bifurcations and instabilities in geomechanics from some of the world`s leading experts. Leading international researchers and practitioners of the topics debate the developments and applications which have occurred over the last few decades.
Описание: Offers insight into the understanding of the nature of the geophysical fluids, especially their structures and structural changes. This book is suitable for graduate students and researchers in fields such as applied mathematics, geophysical fluid dynamics, atmospheric sciences and physical oceanography.
Автор: Simpson David John Warwick Название: Bifurcations In Piecewise-Smooth Continuous Systems ISBN: 9814293849 ISBN-13(EAN): 9789814293846 Издательство: World Scientific Publishing Рейтинг: Цена: 15998.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. This title presents the results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. It reveals various codimension-two, discontinuity induced bifurcations.
Описание: This book introduces the recent developments in the field and provides major advances in fundamental theory of limit cycles. It considers near Hamiltonian systems using Melnikov function as the main mathematical tool.
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