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Towards a Unified Bifurcation Theory


Reference:

Thompson, J. M. T. and Hunt, G. W., 1975. Towards a Unified Bifurcation Theory. Zeitschrift für Angewandte Mathematik und Physik, 26 (5), pp. 581-603.

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Official URL:

http://dx.doi.org/10.1007/BF01594031

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.

Details

Item Type Articles
CreatorsThompson, J. M. T.and Hunt, G. W.
DOI10.1007/BF01594031
DepartmentsFaculty of Engineering & Design > Mechanical Engineering
RefereedYes
StatusPublished
ID Code13238

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