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,
3. `Deterministic Chaos`, H. G. Schuster, 3rd ed.,
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
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%