Practical Bifurcation and Stability Analysis (eBook)

Rüdiger Seydel (Autor)

eBook Download: PDF

2009 | 3rd ed. 2010
XV, 477 Seiten
Springer New York (Verlag)
978-1-4419-1740-9 (ISBN)

Infos

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.

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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.

Inhalt

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.

Produkt-Details

• Reihe/Serie: Interdisciplinary Applied Mathematics
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Schlagworte: Algebra • algorithms • Applied Bifurcation Analysis • Calculus • Chaos • Equilibrium and Chaos • Numerical Algorithms • Numerical bifurcation methods • ordinary differential equation • Periodic Solutions • Practical Bifurcation • Stability Analysis • Test Functions
• ISBN-10: 1-4419-1740-3 / 1441917403
• ISBN-13: 978-1-4419-1740-9 / 9781441917409