Complex network systems - 5AMAC562

Goal(s)

This course in an introduction to complex dynamical systems defined on networks. It aims at bringing to the students an overview of existing technological, social and natural complex systems, together with related issues and problems. Then, the course will provide the students with basic tools for the analysis and deeper understanding of such networks. Students will be asked to gain an operational knowledge by solving periodically problem sets trough supervised work and computer simulations. They will acquire a more advanced knowledge and experience by developing small group projects and paper reviews. Papers and projects topics to be covered will reflect student interest.

Content(s)

• Technological and information networks (internet, grids, information networks, www, etc.)
• Social and biological networks (metabolic, genetic, neural, ecological)
• Mathematics for complex networks (graphs, paths, components, connectivity, etc.)
• Measures and metrics (centrality, communities, assortativity, degree distributions, etc.)
• Algorithms for complex networks(graph generation, network analysis, storing network data, graphs algorithms, models of network formation, etc.)
• Dynamical models defined on networks (cellular automata models, percolation, epidemics, voting models, evolutionary games, traffic models, market models, population models)
• Mean field approaches, bifurcations and chaotic behaviours
• Stability, instability and tipping points /early warnings
• Observation, control and synchronization

The course is intended for any master students in applied science with an undergraduate knowledge in calculus, probability and programming(with any programmation language).