| Relevance of Course Objectives and Core Learning Outcomes(%) |
Teaching and Assessment Methods for Course Objectives |
| Course Objectives |
Competency Indicators |
Ratio(%) |
Teaching Methods |
Assessment Methods |
1. 探討工程與物理等動態系統的數學模式及其穩定性的分析；模式建立與分析的應用亦包含生物、化學及流行病學。
2. 著重於觀察分析線性與非線性系統的結構性改變(structural changes)。
|
| 1.The ability to apply the knowledge of math, science, and mechanical engineering. |
| 2.The ability to design and conduct experiments, as well as to analyze the data obtained. |
| 3.The ability to work with others as a team to design and manufacture products of mechanical engineering systems. |
| 4.The ability humanities awareness and a knowledge of contemporary issues, and to understand the impact of science and engineering technologies, environmental, societal, and global context. |
| 5.The ability of continuing study and self-learning. |
| 6.The knowledge of professional ethics and social responsibilities of a mechanical engineer. |
|
|
|
| Quiz |
| Written Presentation |
| Oral Presentation |
| Assignment |
|
| Course Content and Homework/Schedule/Tests Schedule |
| Week |
Course Content |
| Week 1 |
Introduction: chaos, fractals, dynamics, and importance of being nonlinear.
|
| Week 2 |
One-dimensional flows (systems): geometric ways of thinking, fixed points and stability, structural change, and system potentials. |
| Week 3 |
Bifurcations: saddle-node bifurcation, transcritical bifurcation, supercritical and subcritical pitch-fork bifurcations, imperfect bifurcations and catastrophes.
|
| Week 4 |
Bifurcations: saddle-node bifurcation, transcritical bifurcation, supercritical and subcritical pitch-fork bifurcations, imperfect bifurcations and catastrophes.
|
| Week 5 |
Flows on a circle: uniform and nonuniform oscillators, phase-locking phenomenon.
|
| Week 6 |
Linear 2-D systems: phase portraits, eigenvalues and eigenvectors, classification of stabilities. |
| Week 7 |
Nonlinear 2-D systems: phase portraits, numerical integration and spectral analysis-FFT, fixed points and linearization, conservative systems, reversible systems.
|
| Week 8 |
Nonlinear 2-D systems: phase portraits, numerical integration and spectral analysis-FFT, fixed points and linearization, conservative systems, reversible system. |
| Week 9 |
Midterm exam: in class.
|
| Week 10 |
Limit cycles: Liapunov functions, Poincaré-Bendixson theorem, Liénard systems, relaxation oscillators, weakly nonlinear oscillators.
|
| Week 11 |
Bifurcations revisited in 2-D systems: saddle-node, transcritical, and pitch-fork bifurcations, Hopf bifurcations, oscillating chemical-reactions, hysteresis, quasiperiodic oscillations, Poincaré maps.
|
| Week 12 |
Bifurcations revisited in 2-D systems: saddle-node, transcritical, and pitch-fork bifurcations, Hopf bifurcations, oscillating chemical-reactions, hysteresis, quasiperiodic oscillations, Poincaré maps.
|
| Week 13 |
Duffing’s equation: forced double-well oscillator, a route from periodic oscillation to chaos. |
| Week 14 |
Chaos on 1-D maps and strange attractor: logistic map, period-doubling, Liapunov exponent, orbit diagram and periodic widow, Lorenz map, signal-masking. |
| Week 15 |
Lorenz Equations and other chaotic systems: properties of strange attractor and route to chaos.
|
| Week 16 |
Introduction to fractals: Cantor set, dimension of self-similar fractals, box dimensions, pointwise and correlation dimensions.
|
| Week 17 |
Proposal and discussion for the final project that requires numerical simulations and analyses of a dynamical system selected from published papers or chapters of texts discussing chaotic/fractal behaviors.
|
| Week 18 |
Oral presentation and written report of the final project. |
|
| Evaluation |
作業：30 %
期中考試：30 %
期末報告：40 % |
| Textbook & other References |
教科書: Strogatz, S. H., Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering, 2nd edition, CRC Press, Boca Raton, FL, 2018.
參考書: Moon, F. C., Chaotic Vibrations: An Introduction for Applied Scientists and Engineers, Wiley, New York, 2004. |
| Teaching Aids & Teacher's Website |
數位教學平台iLearning
上課筆記、Power Points, Selected papers |
| Office Hours |
週三 下午 14:00~15:00
|
| Sustainable Development Goals, SDGs |
| 09.Industry, Innovation and Infrastructure 15.Life On Land | include experience courses：N |
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