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.
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: Hale Название: Dynamics and Bifurcations ISBN: 0387971416 ISBN-13(EAN): 9780387971414 Издательство: Springer Рейтинг: Цена: 11313.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The subject of differential and difference equations is an old and much-honored chapter in science, one which germinated in applied fields such as celestial
mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications
with perhaps a more mature look. Many of the available books and expository narratives either require extensive mathematical preparation, or are not designed to be used as
textbooks.
The authors have filled this void with the present book.
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.
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