Towards a Unified Bifurcation Theory
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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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.
|Creators||Thompson, J. M. T.and Hunt, G. W.|
|Departments||Faculty of Engineering & Design > Mechanical Engineering|
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