In dynamics, all continuous time dynamical systems, with and without noise, are Witten-type TQFTs and the phenomenon of the spontaneous breakdown of the corresponding topological supersymmetry encompasses such well-established concepts as chaos, turbulence, 1/f and crackling noises, self-organized criticality etc.
These are all very "deep" phenomena which are studied in continuous-time dynamics, and its somewhat surprising that TQFT has such a wide range of applications. Unfortunately, that wikipedia article doesn't include inline citations, so it isn't clear which source that information comes from. Could someone point to a textbook or review on the applications of TQFT to continuous-time dynamical systems?
EDIT: Is the "topological supersymmetry" bascially the structural stability of the system? That would make sense, except structural stability doesn't imply topological invariance, just invariance under a certain restricted set of diffeomorphisms (i.e. perturbations).