Stability, Instability and Chaos
An Introduction to the Theory of Nonlinear Differential Equations

An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.

Paul Glendinning (Author)

9780521425667, Cambridge University Press

Paperback, published 25 November 1994

404 pages
22.9 x 15.2 x 2.3 cm, 0.59 kg

'The author writes clearly and carefully, weaving together general results with a steady supply of simple examples and excercises for the reader. Pick a section of the book to read at random and one is completely confident that effort is going to be rewarded; that the author is really explaining rather than simply recounting.' The Times Higher Education Supplement

By providing an introduction to nonlinear differential equations, Dr Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincaré-Bendixson theorem, the Hopf bifurcation and chaotic systems. The unique treatment that is found in this book will prove to be an essential guide to stability and chaos.

1. Introduction
2. Stability
3. Linear differential systems
4. Linearization and hyperbolicity
5. Two-dimensional dynamics
6. Periodic orbits
7. Perturbation theory
8. Bifurcation theory I: stationary points
9. Bifurcation theory II: periodic orbits and maps
10. Bifurcational miscellany
11. Chaos
12. Global bifurcation theory.

Subject Areas: Differential calculus & equations [PBKJ]