Chaos bifurcations and fractals around us: a brief introduction
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
River Edge, NJ
World Scientific
©2003
|
| Series: | World Scientific series on nonlinear science
v. 47 |
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | Includes bibliographical references (pages 101-103) and index 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 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 |
| Physical Description: | 1 Online-Ressource (v, 107 pages) |
| ISBN: | 9789812564375 9812564373 |
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| 500 | |a 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 | ||
| 500 | |a 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 | ||
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| isbn | 9789812564375 9812564373 |
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| spelling | Szemplińska-Stupnicka, Wanda Verfasser aut Chaos bifurcations and fractals around us a brief introduction Wanda Szemplińska-Stupnicka River Edge, NJ World Scientific ©2003 1 Online-Ressource (v, 107 pages) txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science v. 47 Includes bibliographical references (pages 101-103) and index 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 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 MATHEMATICS / Differential Equations / General bisacsh Bifurcation theory Chaotic behavior in systems Differential equations, Nonlinear http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=134077 Aggregator Volltext |
| spellingShingle | Szemplińska-Stupnicka, Wanda Chaos bifurcations and fractals around us a brief introduction MATHEMATICS / Differential Equations / General bisacsh Bifurcation theory Chaotic behavior in systems Differential equations, Nonlinear |
| title | Chaos bifurcations and fractals around us a brief introduction |
| title_auth | Chaos bifurcations and fractals around us a brief introduction |
| title_exact_search | Chaos bifurcations and fractals around us a brief introduction |
| title_full | Chaos bifurcations and fractals around us a brief introduction Wanda Szemplińska-Stupnicka |
| title_fullStr | Chaos bifurcations and fractals around us a brief introduction Wanda Szemplińska-Stupnicka |
| title_full_unstemmed | Chaos bifurcations and fractals around us a brief introduction Wanda Szemplińska-Stupnicka |
| title_short | Chaos bifurcations and fractals around us |
| title_sort | chaos bifurcations and fractals around us a brief introduction |
| title_sub | a brief introduction |
| topic | MATHEMATICS / Differential Equations / General bisacsh Bifurcation theory Chaotic behavior in systems Differential equations, Nonlinear |
| topic_facet | MATHEMATICS / Differential Equations / General Bifurcation theory Chaotic behavior in systems Differential equations, Nonlinear |
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