Chaos bifurcations and fractals around us :a brief introduction
- 作者: Szemplińska-Stupnicka, Wanda.
- 出版: River Edge, NJ : World Scientific ©2003.
- 稽核項: 1 online resource (v, 107 pages) :illustrations (some color).
- 叢書名: World Scientific series on nonlinear science. Series A, Monographs and treatises ;v. 47
- 標題: Differential EquationsGeneral. , Electronic books. , Differential equations, Nonlinear. , Chaotic behavior in systems. , Electronic book. , MATHEMATICS , Bifurcation theory. , MATHEMATICS Differential Equations -- General.
- ISBN: 9812386890 , 9789812386892
- ISBN: 9812386890
- 試查全文@TNUA:
- 附註: 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.
- 摘要: 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.
- 電子資源: https://dbs.tnua.edu.tw/login?url=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=134077
- 系統號: 005317902
- 資料類型: 電子書
- 讀者標籤: 需登入
- 引用網址: 複製連結
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.
來源: Google Book
來源: Google Book
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