2018 Networks and Coupled Dynamical Systems

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Academic unit or major
Graduate major in Systems and Control Engineering
Nakao Hiroya 
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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.


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 Learn examples of networks and elementary mathematical models
Class 2 Generative models of networks Understand representative generative models of networks
Class 3 Statistical quantities and spectrum Understand typical statistical quantities and Laplacian spectrum of networks
Class 4 Robustness of networks Understand the notion of network robustness
Class 5 Random walks and diffusion Understand random walks and diffusion on networks
Class 6 Epidemic models Understand representative epidemic models on networks
Class 7 Coupled oscillator networks Understand dynamics of coupled oscillators on networks
Class 8 Self-organization on networks Understand pattern formation on networks


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

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