Details

Subject(s)

• Bifurcation theory [Browse]

Series

• Applied mathematical sciences (Springer-Verlag New York Inc.) ; 112. [More in this series]
• Applied mathematical sciences ; 112

Summary note

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--back cover.

Bibliographic references

Includes bibliographical references (pages 671-690) and index.

Contents

• 1. Introduction to dynamical systems
• 2. Topological equivalence, bifurcations, and structural stability of dynamical systems
• 3. One-parameter bifurcations of equilibria in continuous-time dynamical system
• 4. One-parameter bifurcations of fixed points in discrete-time dynamical systems
• 5. Bifurcations of equilibria and periodic orbits in n-dimensional dynamical systems
• 6. Bifurcations of orbits homoclinic and heteroclinic to hyperbolic equilibria
• 7. Other one-parameter bifurcations in continuous-time dynamical systems
• 8. Two-parameter bifurcations of equilibria in continuous-time dynamical systems
• 9. Two-parameter bifurcations of fixed points in discrete-time dynamical systems
• 10. Numerical analysis of bifurcations
• Appendix A: basic notions from from algebra, analysis, and geometry
• References
• Index.

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ISBN

• 9783031220067 ((hardback))
• 3031220064 ((hardback))

OCLC

1363816545

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