Chaos bifurcations and fractals around us : a brief introduction / Wanda Szemplińska-Stupnicka.

$Cover image for Chaos bifurcations and fractals around us : a brief introduction / Wanda Szemplińska-Stupnicka.$

ISBN:

9789812564375

Title:

Chaos bifurcations and fractals around us : a brief introduction / Wanda Szemplińska-Stupnicka.

Author:

Szemplińska-Stupnicka, Wanda.

Personal Author:

Szemplińska-Stupnicka, Wanda.

Publication Information:

Physical Description:

1 online resource (v, 107 pages) : illustrations (some color).

Series:

World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 47

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.

Local Note:

eBooks on EBSCOhost

Subject Term:

Bifurcation theory.

Chaotic behavior in systems.

Differential equations, Nonlinear.

Format:

Electronic Resources

Electronic Access:

Click here to view

Publication Date:

2003

Publication Information:

Available:*

Shelf Number	Material Type	Copy	Shelf Location	Status
515.35 22	1:E-BOOK	1	1:ONLINE	Searching... Unknown

Bound With These Titles

On Order

Summary

During the last twenty years, a large number of books on nonlinear chaotic dynamics in deterministic dynamical systems have appeared. These academic tomes are intended for graduate students and require a deep knowledge of comprehensive, advanced mathematics. There is a need for a book that is accessible to general readers, a book that makes it possible to get a good deal of knowledge about complex chaotic phenomena in nonlinear oscillators without deep mathematical study.Chaos, Bifurcations and Fractals Around Us: A Brief Introduction fills that gap. It is a very short monograph that, owing to geometric interpretation complete with computer color graphics, makes it easy to understand even very complex advanced concepts of chaotic dynamics. This invaluable publication is also addressed to lecturers in engineering departments who want to include selected nonlinear problems in full time courses on general mechanics, vibrations or physics so as to encourage their students to conduct further study.