Nonlinear dynamics of spatio-temporal processes in complex systems
The author attempts to synthesize into a geometrical framework several theoretical programs that address issues of pattern formation. The most prominent of these programs are Sattinger's bifurcation theory, Haken's synergetics, and Arnol'd's singularity theory. Using representative examples, the author shows how topological singularities and bifurcation processes deriving from the principal of structural stability determine the dominating features and phenomena observed in both structure formation and form recognition. Because they are universal and classifiable, these geometric bifurcation processes also facilitate qualitative analogies between the critical behavior of nonlinear systems of various origins.
scientific article; zbMATH DE number 571384