Elements of Applied Bifurcation Theory
Seiten
1998
|
2nd Revised edition
Springer-Verlag New York Inc.
978-0-387-98382-0 (ISBN)
Springer-Verlag New York Inc.
978-0-387-98382-0 (ISBN)
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This title provides a solid basis in non-linear dynamical systems and their bifurcations, giving the necessary understanding of the approaches, methods, results and terminology used in the modern applied mathematics literature. This new edition updates theoretical and software developments.
This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special attention is given to efficient numerical implementations of the developed techniques. Several examples from recent research papers are used as illustrations. The book is designed for advanced undergraduate or graduate students in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the previous editions, while updating the context to incorporate recent theoretical and software developments and modern techniques for bifurcation analysis. Review of previous editions: "I know of no other book that so clearly explains the basic phenomena of bifurcation theory."
- Math Reviews "The book is a fine addition to the dynamical systems literature. It is good to see, in our modern rush to quick publication, that we, as a mathematical community, still have time to bring together, and in such a readable and considered form, the important results on our subject." - Bulletin of the AMS "It is both a toolkit and a primer" - UK Nonlinear News
This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special attention is given to efficient numerical implementations of the developed techniques. Several examples from recent research papers are used as illustrations. The book is designed for advanced undergraduate or graduate students in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the previous editions, while updating the context to incorporate recent theoretical and software developments and modern techniques for bifurcation analysis. Review of previous editions: "I know of no other book that so clearly explains the basic phenomena of bifurcation theory."
- Math Reviews "The book is a fine addition to the dynamical systems literature. It is good to see, in our modern rush to quick publication, that we, as a mathematical community, still have time to bring together, and in such a readable and considered form, the important results on our subject." - Bulletin of the AMS "It is both a toolkit and a primer" - UK Nonlinear News
Introduction to Dynamical Systems * Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems * One-Parameter Bifurcations of Equilibria in Continuous-Time Systems * One-Parameter Bifurcations of Fixed Points in Discrete-Time Systems * Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Systems * Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria * Other One-Parameter Bifurcations in Continuous-Time Systems * Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems * Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems * Numerical Analysis of Bifurcations * A: Basic Notions from Algebra, Analysis, and Geometry * References * Index.
| Reihe/Serie | Applied Mathematical Sciences ; v. 112 |
|---|---|
| Zusatzinfo | 251 illustrations, references, index |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-10 | 0-387-98382-1 / 0387983821 |
| ISBN-13 | 978-0-387-98382-0 / 9780387983820 |
| Zustand | Neuware |
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