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
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
|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
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