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＜E-Book＞
Practical Bifurcation and Stability Analysis / by Rüdiger U. Seydel
(Interdisciplinary Applied Mathematics. ISSN:21969973 ; 5)

Edition	3rd ed. 2010.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2010
Language	English
Size	XV, 477 p. 200 illus : online resource
Authors	*Seydel, Rüdiger U author SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Engineering mathematics LCSH:Engineering -- Data processing  All Subject Search LCSH:Mathematical physics LCSH:Numerical analysis FREE:Dynamical Systems FREE:Mathematical and Computational Engineering Applications FREE:Mathematical Methods in Physics FREE:Numerical Analysis
Notes	and Prerequisites -- Basic Nonlinear Phenomena -- Applications and Extensions -- Principles of Continuation -- Calculation of the Branching Behavior of Nonlinear Equations -- Calculating Branching Behavior of Boundary-Value Problems -- Stability of Periodic Solutions -- Qualitative Instruments -- Chaos This book covers the central role that bifurcations play in nonlinear phenomena, explaining mechanisms of how stability is gained or lost. It emphasizes practical and computational methods for analyzing dynamical systems. A wide range of phenomena between equilibrium and chaos is explained and illustrated by examples from science and engineering. The book is a practical guide for performing parameter studies and includes exercises. Combining an introduction on the textbook level with an exposition of computational methods, this book addresses the mathematical needs of scientists and engineers. It should be of interest to those in a wide variety of disciplines, including physics, mechanical engineering, electrical engineering, chemistry and chemical engineering, biology, and medicine. Both graduate students (in courses on dynamical systems, stability analysis, differential equations, and chaos) and professionals will be able to use the book equally well. The introduction avoids mathematical formalism, and the only required background is calculus. In the third edition there is a chapter on applications and extensions of standard ODE approaches, for example, to delay equations, to differential-algebraic equations, and to reaction-diffusion problems. Additional material is inserted, including the topics deterministic risk, pattern formation, and control of chaos, and many further references. Review of Earlier Edition: "The outcome is impressive. The book is beautifully written in a style that seeks not only to develop the subject matter but also to expose the thought processes behind the mathematics." Proceedings of the Edinburgh Mathematical Society HTTP:URL=https://doi.org/10.1007/978-1-4419-1740-9

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