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School of Environment and Society
- Department of Architecture and Building Engineering
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- Graduate major in Technology and Innovation Management
- 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 (Livestream)
- Media-enhanced courses
- Day/Period(Room No.)
- Mon5-6()
- Group
- -
- Course number
- SCE.A404
- Credits
- 1
- Academic year
- 2022
- Offered quarter
- 2Q
- Syllabus updated
- 2022/3/16
- Lecture notes updated
- -
- Language used
- English
- Access Index
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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 | 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 | Emergence of chaotic dynamics and its characterization |
Out-of-Class Study Time (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.
Assessment criteria and methods
Grading will be based on the homework scores.
Related courses
- MTH.C341 ： Differential Equations I
- MTH.C342 ： Differential Equations II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Elementary knowledge of mathematics and physics
