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.
ISBN
9783031220067 ((hardback))
3031220064 ((hardback))
OCLC
1363816545
Statement on language in description
Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
Read more...