2024 Faculty Courses School of Engineering Department of Systems and Control Engineering Graduate major in Systems and Control Engineering
Nonlinear Dynamics
- Academic unit or major
- Graduate major in Systems and Control Engineering
- Instructor(s)
- Hiroya Nakao
- Class Format
- Lecture (Blended)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Mon
- Class
- -
- Course Code
- SCE.A404
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
Various real-world phenomena are modeled as dynamical systems. In this course, starting with the elements of dynamical systems theory, destabilization of stationary states and emergence of spontaneous rhythmic or chaotic dynamics are explained, using mathematical models of real-world systems as examples.
Course description and aims
The aim of this course is to provide knowledge on the elements of dynamical systems theory such as stability and bifurcation, as well as on the dynamical systems modeling of real-world phenomena. In particular, theoretical and numerical analysis of nonlinear oscillations will be discussed.
Keywords
Dynamical systems, stability, nonlinear oscillations, chaos, synchronization
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
lectures, homework
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Introduction / Phase space and flows |
Notion of phase space and flows |
| Class 2 | Gradient, Hamiltonian, and one-dimensional dynamical systems |
Dynamics of gradient, Hamiltonian, and one-dimensional dynamical systems |
| Class 3 | Stability and bifurcation |
Notions of stability, linear stability analysis and bifurcation of fixed points |
| Class 4 | 2-dimensional systems |
Dynamics on the two-dimensional phase plane |
| Class 5 | Limit-cycle oscillations |
Emergence of limit-cycle oscillations and typical examples |
| Class 6 | Reduction methods and synchronization |
Methods to simplify dynamical systems and analyzing synchronization phenomena of nonlinear oscillations |
| Class 7 | Chaotic dynamics / Dynamics of networked systems |
Emergence of chaotic dynamics and its characterization / collective dynamics of networked systems |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 60 minutes for reviewing the class content afterwards (including assignments) for each class by referring to textbooks and other course material.
Textbook(s)
None specified.
Reference books, course materials, etc.
Steven Strogatz, "Nonlinear dynamics and chaos", Westview press.
Kuramoto, "Chemical Oscillations, Waves, and Turbulence", Springer.
Hoppensteadt & Izhikevich, "Weakly Connected Neural Networks", Springer.
Evaluation methods and criteria
Grading will be based on the homework scores.
Related courses
- MTH.C341 ： Differential Equations I
- MTH.C342 ： Differential Equations II
Prerequisites
Elementary knowledge of applied mathematics and physics