Скачать или смотреть 8. Dynamical Systems: Replicator Dynamics & Spatial Extension, Lyapunov Function, Diffusion Equation

Self-Organization and Pattern Formation, Prof. Erwin Frey, LMU Munich, Winter Semester 2025/2026

Can we build predictive theories for self-organizing systems—spanning fluids, diffusion–reaction systems, soft/active matter, and living systems—without tracking every microscopic detail? Yes: by exploiting universality, symmetry, and conservation laws, and coarse-graining to reveal instability mechanisms, mesoscopic laws, and scaling behavior.

This lecture covers spatially extended nonequilibrium systems that spontaneously generate order. Emphasis on the onset of instability, pattern selection, dynamics, and the emergence of mesoscopic laws. Methods include dynamical systems, continuum field theories, statistical physics, weakly nonlinear analysis, and differential geometry.