Averaging Methods in Nonlinear Dynamical Systems, Sanders J. A., Verhulst F., Murdock J.

Автор: Wiggins
Название: Introduction to Applied Nonlinear Dynamical Systems and Chaos
ISBN: 0387001778 ISBN-13(EAN): 9780387001777
Издательство: Springer
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Цена: 93160.00 T
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Описание: This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as students of mathematics. This new edition contains extensive new material on invariant manifold theory and normal forms (in particular, Hamiltonian normal forms and the role of symmetry). Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography as well as a detailed glossary of terms, making it a comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of view.

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: Haddad, Wassim M. Chellaboina, Vijaysekhar
Название: Nonlinear dynamical systems and control
ISBN: 0691133298 ISBN-13(EAN): 9780691133294
Издательство: Wiley
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Цена: 149950.00 T
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Описание: Presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. This graduate-level textbook is suitable for applied mathematicians, dynamical systems theorists, control theorists, and engineers.

Автор: Chiang
Название: Stability Regions of Nonlinear Dynamical Systems
ISBN: 1107035406 ISBN-13(EAN): 9781107035409
Издательство: Cambridge Academ
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Цена: 163680.00 T
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Описание: In this comprehensive and authoritative work, leading researchers describe theory and optimal estimation, propose new concepts, and detail relevant practical applications. This is the first book on the subject, and it is an invaluable resource for academics, researchers and professional engineers.