Dynamical Systems Seminar

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Stochastic Spatial Patterns: From Fundamental Waves to Complex Structures

Speaker: Christian Kuehn, Technical University of Munich

Location: Warren Weaver Hall 705

Date: Wednesday, October 14, 2026, 3:30 p.m.

Synopsis:

Spatially extended systems in biology, neuroscience, and physics are inherently affected by randomness, prompting the need for a dynamical systems theory of stochastic partial differential equations (SPDEs). This talk surveys recent advances on stochastic travelling and rotating wave solutions in reaction-diffusion SPDEs. We present rigorous robustness results showing that deterministic Nagumo travelling fronts persist under small stochastic perturbations, together with a multiscale description of phase diffusion in stochastic FitzHugh-Nagumo pulse propagation. A further result demonstrates noise-induced synchronization of travelling waves, where initially shifted pulses converge due to stochastic effects. Moving to two spatial dimensions, we discuss rotating and spiral waves and derive effective finite-dimensional stochastic dynamics governing their phase evolution. These results yield quantitative large-deviation estimates for stability and first-exit problems, illustrating how deterministic wave theory and stochastic analysis combine to explain pattern persistence and stochastic deformation in complex spatial systems.