Nonlinear and Complex Systems (141476-WiSe25/26)

GOALS:

After successful completion of the course, the students

• apply phase plane analysis to few-dimensional nonlinear systems,
• analyze linear instabilities and identify nonlinear stationary states of pattern-forming systems,
• incorporate stochastic effects via models of evolutionary dynamics,
• identify global characteristics through order parameters and symmetry breaking,
• gain familiarity with the systems-level approach of network science.

CON­TENT:

This course provides a comprehensive introduction to nonlinear, pattern-forming, and complex dynamic systems. Starting with an introduction to nonlinear systems theory (one-dimensional systems, two-dimensional systems, bifurcations, chaos, fractals), it will proceed to discuss pattern formation (Swift-Hohenberg and complex Ginzburg Landau eqn's), adaptive dynamics (fitness landscapes, evolutionary game theory), and finally, the concepts and techniques from non-equilibrium statistical physics (phase transitions, order parameters, symmetry breaking, statistical field theory) and complex networks (random, scale-free networks, preferential attachment). It will emphasise analytical methods and geometric thinking supported by numerical techniques.

EXAM:

Oral exam (30 min.)

Registration: FlexNow