動態系統

This course aims to teach some fundamentals of dynamical systems as continuous/discrete time, a subject related to many branches of pure/applied mathematics and applied science. We will introduce methods to analyze the qualitative behavior of solutions on nonlinear dynamical systems, e.g., phase space analysis, bifurcation theory, the notion of limit cycles, fractals, strange attractors, and chaos. Some applications will be given. Besides, another goal of this course is to train the students to improve their presentation ability in English.

Calculus (along with multivariable calculus ), Advanced Calculus, Linear Algebra, ODE (not a prerequisite)

Homework 40% Presentation 30% Final Exam 30%

• Stability and Linearization
• Lyapunov Functions
• Bifurcations
• Limit Cycles
• Bifurcations Revisited
• One-Dimensional Maps
• Fractals
• The Smale Horseshoe
• Symbolic Dynamics
• Strange Attractors

We will not follow a single textbook, but a list of recommended reading materials as follows: References: J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, 1983. R. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd edition, 2003. S. Strogatz, Nonlinear Dynamics and Chaos With Applications to Physics, Biology, Chemistry, and Engineering, 2nd Ed. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, NY, 1990 Sze-Bi Hsu, Ordinary Differential Equations with Applications, World Scientific Press, 2013 (Second edition)

地點

SA236 or online meeting

時間

By appointment.

聯絡方式

email: changhong@math.nctu.edu.tw