課程資訊
 課程名稱 混沌力學導論INTRODUCTION TO CHAOTIC DYNAMICS 開課學期 96-1 授課對象 工學院  機械工程學系 授課教師 伍次寅 課號 ME5134 課程識別碼 522 U1660 班次 學分 3 全/半年 半年 必/選修 選修 上課時間 星期四6,7,8(13:20~16:20) 上課地點 工綜205 備註 總人數上限：40人 課程網頁 http://www.me.ntu.edu.tw/course/word/522U1660.doc 課程簡介影片 核心能力關聯 核心能力與課程規劃關聯圖 課程大綱 為確保您我的權利,請尊重智慧財產權及不得非法影印 課程概述 課號：522 U1660 班次： 主授教授：伍次寅 學分： 3 課程名稱：混沌力學導論 (Introduction to Chaotic Dynamics) 教科書：1. `Chaos and Nonlinear Dynamics`, 2nd ed., R.C. Hilborn, 2000, Oxford Univ. Press. 2. `Nonlinear Dynamics and Chaos`, S. H. Strogatz, 1994, Addison-Wesley. 3. `Deterministic Chaos`, H. G. Schuster, 3rd ed., 1995, VCH. 課程大綱： 1. Introduction: The name of the new science and origin of `chaos`. Is chaos a generic or pathological phenomenon? 2. Phenomenology of chaos: three physical examples (and many others) demonstrating chaotic motions, bifurcations, `strange attractors`, fractals, metaphor of `butterfly effect`, universality of chaos. 3. Dynamical systems and state-space dynamics: (in which `chaos` is dwelt) Topics include linear and nonlinear stabilities, bifurcations, phase portraits, qualitative theories of dynamical systems. 4. Routes to chaos: (via which chaotic motions emerge) Topics include period-doubling bifurcation, quasi-periodicity bifurcation, intermittency, crises, chaotic transient (homoclinic bifurcation). 5. Measures of chaos: (identifying and quantifying chaos) Fourier spectrum, correlation function, Lyapunov exponent, Poincare section, return-map method. 6. Iterated maps and their complicated dynamics: (a simple yet generic way to generate chaotic motions) quadratic map, renormalization theory, tent map, Baker`s map, circle map, Henon map, Smale horseshoe map, mathematical definition of `strong chaos`, concept of `topological equivalence`, hyperbolic intersections and applications of symbolic dynamics, statistical description of chaotic trajectories. 7. Fractals: (the most generic way the nature assumes its pattern) examples of mathematical fractals and physical fractals, self-similarity, fractal dimensions, correlation dimension, generalized dimension of fractal, mono- and multifractal, fractal basin boundaries, fractal attractors, Cantor set, Mandelbrot set, fractals on everything at everywhere. 8. Advanced topics: synchronization of chaotic motions, chaos control, embedding theory, state-space reconstruction technique, nonlinear time-series analysis 成績評量方式： 1. 作業報告(short report)(1~2次) 佔 25% 2. 期中考(1次) 佔 35~40% 3. 期末實作計劃(term project) 佔 35~40% 課程目標 課程要求 預期每週課後學習時數 Office Hours 指定閱讀 參考書目 評量方式(僅供參考)
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