Practical Bifurcation and Stability Analysis

1. Front Matter

   Pages i-xv

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2. Introduction and Prerequisites

   • Rüdiger Seydel

   Pages 1-52

3. Basic Nonlinear Phenomena

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   Pages 53-115

4. Applications and Extensions

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   Pages 117-167

5. Principles of Continuation

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   Pages 169-198

6. Calculation of the Branching Behavior of Nonlinear Equations

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   Pages 199-261

7. Calculating Branching Behavior of Boundary-Value Problems

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   Pages 263-302

8. Stability of Periodic Solutions

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   Pages 303-356

9. Qualitative Instruments

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   Pages 357-384

10. Chaos

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    Pages 385-423

11. Back Matter

    Pages 1-57

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Fifteen years have elapsed after the second edition of Practical Bifurcation and Stability Analysis was published. During that time period the ?eld of computational bifurcation has become mature. Today, bifurcation mec- nisms are widely accepted as decisive phenomena for explaining and - derstanding stability and structural change. Along with the high level of sophistication that bifurcation analysis has reached, the research on basic computational bifurcation algorithms is essentially completed, at least in - dinary di?erential equations. The focus has been shifting from mathematical foundations towards applications. The evolution from equilibrium to chaos has become commonplace and is no longer at the cutting edge of innovation. But the corresponding methods of practical bifurcation and stability analysis remain indispensable instruments in all applications of mathematics. This constant need for practical bifur- tion and stability analysis has stimulated an e?ort to maintain this book on a present-day level. The author’s endeavor has resulted in this third edition. It is based on more than three decades of practical experience with the subject, and on many courses given at several universities.

• Algebra
• Applied Bifurcation Analysis
• Equilibrium and Chaos
• Numerical Algorithms
• Numerical bifurcation methods
• Periodic Solutions
• Practical Bifurcation
• Stability Analysis
• Test Functions
• algorithms
• calculus
• chaos
• ordinary differential equation

From the reviews of the third 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

“Methods of practical bifurcation and stability analysis are crucial instruments in applied mathematics. This fact stimulated the author to publish an up-to-date third edition, sixteen years after appearing the second edition. … The references contain more than 600 items. The excellent presentation of the material will stimulate people in applied sciences to apply the well-prepared instruments.” (Klaus R. Schneider, Zentralblatt MATH, Vol. 1195, 2010)

• Mathematisch-Naturwiss. Fakultät, Universität Köln, Köln, Germany

  Rüdiger Seydel

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