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Interdisciplinary Applied Mathematics #5: Practical Bifurcation and Stability Analysis

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Synopses & Reviews

Publisher Comments:

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

Synopsis:

This book contains computational methods for numerically computing steady state and Hopf bifurcations. It is probably the first textbook to describe these types of numerical bifurcation techniques. The book requires only a basic knowledge of calculus, and uses detailed examples, problems, and figures. This will be appropriate as a textbook for graduate students.

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.

Synopsis:

Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.

Table of Contents

Contents: Preface.- Notation.- Introduction 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.- Appendices.- List of Major Examples.- References.- Index.

Product Details

ISBN:
9781441917393
Author:
Seydel, Rudiger
Publisher:
Springer
Author:
Seydel, Ra1/4diger
Author:
Seydel, Rudiger U.
Subject:
Mathematical Analysis
Subject:
Number Systems
Subject:
Mathematical Physics
Subject:
Mathematics-Analysis General
Subject:
Applied Bifurcation Analysis
Subject:
Equilibrium and Chaos
Subject:
Numerical Algorithms
Subject:
Numerical bifurcation methods
Subject:
periodic solutions
Subject:
Practical Bifurcation
Subject:
Stability Analysis
Subject:
Test Functions
Subject:
Dynamical Systems and Ergodic Theory
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
mathematical methods in physics
Subject:
Numerical analysis
Copyright:
Edition Description:
3rd ed. 2010
Series:
Interdisciplinary Applied Mathematics
Series Volume:
5
Publication Date:
20091214
Binding:
HARDCOVER
Language:
English
Pages:
492
Dimensions:
235 x 155 mm 1940 gr

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Interdisciplinary Applied Mathematics #5: Practical Bifurcation and Stability Analysis New Hardcover
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Product details 492 pages Springer - English 9781441917393 Reviews:
"Synopsis" by , This book contains computational methods for numerically computing steady state and Hopf bifurcations. It is probably the first textbook to describe these types of numerical bifurcation techniques. The book requires only a basic knowledge of calculus, and uses detailed examples, problems, and figures. This will be appropriate as a textbook for graduate students.

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.

"Synopsis" by , Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.
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