Nonlinear Dynamics: A Primer
Cambridge University Press
Edition: Illustrated, 10/11/2001
EAN 9780521558747, ISBN10: 0521558743
Paperback, 316 pages, 24.4 x 17 x 1.8 cm
Language: English
A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selected book exercises. See www.cambridge.org/economics/resources
1. Statics and dynamics
some elementary concepts
2. Review of linear systems
3. Stability of fixed points
4. Invariant and attracting sets, periodic and quasiperiodic orbits
5. Local bifurcations
6. Chaotic sets and chaotic attractors
7. Characteristic exponents, fractals, homoclinic orbits
8. Transition to chaos
9. The ergodic approach
10. Deterministic systems and stochastic processes.