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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

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Release : 2013-11-21
Genre : Mathematics
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Book Rating : 409/5 ( reviews)

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Book Synopsis Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by : John Guckenheimer

Download or read book Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields written by John Guckenheimer. This book was released on 2013-11-21. Available in PDF, EPUB and Kindle. Book excerpt: An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Nonlinear Oscillations and Waves in Dynamical Systems

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Release : 2013-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 639/5 ( reviews)

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Book Synopsis Nonlinear Oscillations and Waves in Dynamical Systems by : P.S Landa

Download or read book Nonlinear Oscillations and Waves in Dynamical Systems written by P.S Landa. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

Dynamical Systems And Nonlinear Oscillations - Proceedings Of The Symposium

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Release : 1986-01-01
Genre :
Kind : eBook
Book Rating : 288/5 ( reviews)

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Book Synopsis Dynamical Systems And Nonlinear Oscillations - Proceedings Of The Symposium by : G Ikegami

Download or read book Dynamical Systems And Nonlinear Oscillations - Proceedings Of The Symposium written by G Ikegami. This book was released on 1986-01-01. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields

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Release : 1986
Genre :
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Book Rating : /5 ( reviews)

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Book Synopsis Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields by : John M. Guckenheimer

Download or read book Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields written by John M. Guckenheimer. This book was released on 1986. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Differential Equations and Dynamical Systems

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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 490/5 ( reviews)

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Book Synopsis Nonlinear Differential Equations and Dynamical Systems by : Ferdinand Verhulst

Download or read book Nonlinear Differential Equations and Dynamical Systems written by Ferdinand Verhulst. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.

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