Methods for Complex Systems Science: Dynamical Systems

Catalog description

Focuses on the mechanisms through which complexity emerges in evolving and dynamical network architectures. Some of the best-known examples include gene expression networks, adaptive ecological networks, and neural networks for cognitive information processing. Complex systems theory deals with dynamical systems with a large number of interacting variables. Therefore, after an introduction to graph and network theory, the course covers the basic concepts of dynamical systems theory: continuous and discrete systems, attractor dynamics, bifurcation, and chaos. After introducing information theory, devoted to the fundamentals, the second part focuses on applications, especially to network dynamics. Students acquire familiarity through the analysis of concrete examples of both deterministic and random dynamics in the form of Boolean networks and random walks.