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.
LanguageEnglish
Pages581-603
Number of pages23
JournalZeitschrift für Angewandte Mathematik und Physik
Volume26
Issue number5
DOIs
StatusPublished - Sep 1975

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Bifurcation Theory
catastrophe theory
Cosmology
psychology
Crystallography
delineation
biology
quantitative analysis
Catastrophe theory
crystallography
cosmology
Hydrodynamics
hydrodynamics
Thermodynamics
Imperfections
Unification
Quantitative Analysis
Discrete Systems
perturbation
thermodynamics

Cite this

Towards a Unified Bifurcation Theory. / Thompson, J M T; Hunt, Giles W.

In: Zeitschrift für Angewandte Mathematik und Physik, Vol. 26, No. 5, 09.1975, p. 581-603.

Research output: Contribution to journalArticle

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