Towards a Unified Bifurcation Theory

J M T Thompson, Giles W Hunt

Research output: Contribution to journalArticle

Abstract

Bifurcation theories for the instability of slowly evolving systems have been developed in various disciplines, and a first step is here taken towards some desirable unification. A modern account of the authors' general branching theory for discrete systems is first presented, some new features being the introduction of principal imperfections and the delineation of the important semi-symmetric points of bifurcation. This theory, embedded in a perturbation approach ideal for quantitative analysis, is complementary to the far-reaching qualitative catastrophe theory of René Thom which offers a profound topological classification of instability phenomena. For this reason, we present here a detailed correlation of the two theories. Also presented in the paper is a survey of some fields of application ranging from classical fields such as hydrodynamics, through thermodynamics, crystallography and cosmology, to the newer domains of biology and psychology.
Original languageEnglish
Pages (from-to)581-603
Number of pages23
JournalZeitschrift für Angewandte Mathematik und Physik
Volume26
Issue number5
DOIs
Publication statusPublished - Sep 1975

Fingerprint Dive into the research topics of 'Towards a Unified Bifurcation Theory'. Together they form a unique fingerprint.

Cite this