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School of Engineering
- Undergraduate major in Mechanical Engineering
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- Common courses
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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
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
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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
- Media-enhanced courses
- Day/Period(Room No.)
- Thr7-8(W831)
- Group
- -
- Course number
- SCE.A501
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 4Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- 2020/1/16
- Language used
- English
- Access Index
-
Course description and aims
Coupled dynamical systems on networks are universal understructures of the real world. In this course, starting with elementary facts on the network (graph) theory, typical generative models of networks, characterization of networks by the spectrum and other statistical quantities, and properties of coupled dynamical systems on networks will be discussed.
Student learning outcomes
The aim of this course is to learn the elements of networks and coupled dynamical systems and to understand how to mathematically model and analyze real-world dynamical systems on networks.
Keywords
Networks (graphs), spectrum, random walks, diffusion, synchronization, nonlinear dynamics
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 | Learning examples of networks (graphs) and basic methods of mathematical description |
| Class 2 | Generative models of networks | Understanding representative generative models of networks |
| Class 3 | Graph Laplacian and random walks | Understanding graph Laplacian and random walks |
| Class 4 | Epidemic models on networks | Understanding representative epidemic models on networks |
| Class 5 | Coupled oscillator networks | Understanding dynamics of coupled oscillators on networks |
| Class 6 | Chaotic synchronization | Understanding chaotic synchronization on networks |
| Class 7 | Self-organization and pattern formation on networks | Understanding self-organization and pattern formation on networks |
Textbook(s)
Newman, "Networks", Oxford
Reference books, course materials, etc.
Barrat, Barthelemy, Vespignani, "Dynamical Processes on Complex Networks", Cambridge.
Dorogovtsev, "Lectures on complex networks", Oxford
Assessment criteria and methods
Grading will be based on homework scores.
Related courses
- SCE.A404 ： Nonlinear Dynamics
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Elementary knowledge of mathematics and physics
