課程資訊
課程名稱
混沌力學導論
INTRODUCTION TO CHAOTIC DYNAMICS 
開課學期
95-1 
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
全/半年
半年 
必/選修
選修 
上課時間
星期二6,7,8(13:20~16:20) 
上課地點
工綜B04 
備註
總人數上限:40人 
 
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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%
 

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