Chaos bifurcations and fractals around us : a brief introduction /
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
River Edge, NJ :
World Scientific,
©2003.
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| Series: | World Scientific series on nonlinear science. Series A, Monographs and treatises ;
v. 47 |
| Subjects: | |
| Online Access: | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=134077 |
Table of Contents:
- 1. Introduction
- 2. Ueda's "strange attractors"
- 3. Pendulum. 3.1. Equation of motion, linear and weakly nonlinear oscillations. 3.2. Method of Poincaré map. 3.3. Stable and unstable periodic solutions. 3.4. Bifurcation diagrams. 3.5. Basins of attraction of coexisting attractors. 3.6. Global homoclinic bifurcation. 3.7. Persistent chaotic motion
- chaotic attractor. 3.8. Cantor set
- an example of a fractal geometric object
- 4. Vibrating system with two minima of potential energy. 4.1. Physical and mathematical model of the system. 4.2. The single potential well motion. 4.3. Melnikov criterion. 4.4. Fractal boundaries of basins of attraction and transient chaos in the region of principal resonance. 4.5. Oscillating chaos and unpredictability of the final state after destruction of the resonant attractor. 4.6. Boundary crisis of the oscillating chaotic attractor. 4.7. Persistent cross-well chaos. 4.8. Lyapunov exponents. 4.9. Intermittent transition to chaos. 4.10. Large orbit and the boundary crisis of the cross-well chaotic attractor. 4.11. Various types of attractors of the two-well potential system
- 5. Closing remarks.