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- 工学院，物質理工学院，環境・社会理工学院共通科目
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- School of Science
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School of Environment and Society
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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Systems and Control Engineering
- Instructor(s)
- Nakao Hiroya
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Thr7-8(W934)
- Group
- -
- Course number
- SCE.A404
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 3Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
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.
Student learning outcomes
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 that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
lectures, homework
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Introduction / Phase space and flows | Understand the notion of phase space and flows |
| Class 2 | One-dimensional dynamical systems | Understand the dynamics of one-dimensional systems |
| Class 3 | Two-dimensional dynamical systems | Understand the dynamics on the two-dimensional phase plane |
| Class 4 | Stability and bifurcation | Understand the linear stability analysis and destabilization of fixed points |
| Class 5 | Limit-cycle oscillations | Understand the emergence of limit-cycle oscillations and typical examples |
| Class 6 | Reduction methods | Understand the methods to simplify dynamical systems |
| Class 7 | Synchronization | Understand the synchronization phenomena of nonlinear oscillations |
| Class 8 | Chaos | Understand the emergence of chaos and its characterization |
Textbook(s)
Steven Strogatz, "Nonlinear dynamics and chaos", Westview press.
Reference books, course materials, etc.
Kuramoto, "Chemical Oscillations, Waves, and Turbulence", Springer.
Hoppensteadt & Izhikevich, "Weakly Connected Neural Networks", Springer.
Assessment criteria and methods
Grading will be based on the homework scores.
Related courses
- SCE.A501 ： Networks and Coupled Dynamical Systems
- MTH.C341 ： Differential Equations I
- MTH.C342 ： Differential Equations II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Elementary knowledge of mathematics and physics
