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Bifurcation and hysteresis varieties for the thermal-chainbranching model with a negative modal parameter

  • Ian N. Stewart (a1)
Abstract

The theory of unfoldings of singularities, or ‘elementary catastrophe theory’ (Thom(10), Poston and Stewart(9), Golubitsky and Guillemin(3), Gibson(2)) has been generalized by Golubitsky and Schaeffer(5,6), providing a powerful method for analysing imperfect bifurcation. One recent application by Golubitsky, Keyfitz, and Schaeffer(4) concerns the ‘explosion peninsula’ in chemical reactions such as that between hydrogen and oxygen. They show that the ‘thermal-chainbranching model’ of Gray and Yang(7,8) is capable of reproducing the necessary qualitative features, a result for which only heuristic arguments had previously been available.

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(3) M. Golubitsky and V. Guillemin Stable Mappings and their Singularities (Springer-Verlag, Berlin, Heidelberg, New York, 1973).

(5) M. Golubitsky and D. Schaeffer A theory for imperfect bifurcation via singularity theory. Commun. Pure Appl. Math. 32 (1979), 2198.

(6) M. Golubitsky and D. Schaeffer Imperfect bifurcation in the presence of symmetry. Commun. Math. Phys. 67 (1979), 205232.

(7) B. F. Gray Theory of branching reactions with chain interaction. Trans. Faraday Soc. 66 (1970), 11181126.

(8) B. F. Gray and C. H. Yang On the unification of the thermal and chain theories of explosion limits. J. Phys. Chem. 69 (1965) 2747.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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