2019 Networks and Coupled Dynamical Systems

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Academic unit or major
Graduate major in Systems and Control Engineering
Nakao Hiroya 
Class Format
Media-enhanced courses
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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 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


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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