Nonlinear dynamics of spatio-temporal processes in complex systems
type: Item
instance of: scholarly article
title: Nonlinear dynamics of spatio-temporal processes in complex systems
zbMATH Open document ID: 0798.58052
DOI: 10.1016/0895-7177(94)90115-5
published in: Mathematical and Computer Modelling
publication date: 1994-11-03T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 58-02
zbMATH DE Number: 571384
zbMATH Keywords: pattern formation
zbMATH Keywords: bifurcation
zbMATH Keywords: structural stability
author: Alessandro L. Kovacs
reviewed by: William J. Satzer Jr.
MaRDI profile type: Publication
full work available at URL: 0895-7177(94)90115-5
OpenAlex ID: W2047451189
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description: scientific article; zbMATH DE number 571384