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.
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
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
|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
Barrat, Barthelemy, Vespignani, "Dynamical Processes on Complex Networks", Cambridge.
Dorogovtsev, "Lectures on complex networks", Oxford
Grading will be based on homework scores.
Elementary knowledge of mathematics and physics