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

Published online by Cambridge University Press:  24 October 2008

Ian N. Stewart
Ian N. Stewart
Affiliation:
University of Warwick
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 1 , July 1981 , pp. 127 - 139
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Callahan, J.Special bifurcations of the double cusp (preprint), (University of Warwick, 1978).Google Scholar
(2)Gibson, C. G.Singular points of Smooth Mappings (Research Notes in Mathematics 25, Pitman, London and Boston 1979).Google Scholar
(3)Golubitsky, M. and Guillemin, V.Stable Mappings and their Singularities (Springer-Verlag, Berlin, Heidelberg, New York, 1973).CrossRefGoogle Scholar
(4)Golubitsky, M., Keyfitz, B. and Schaeffer, D. A Singularity Theory analysis of a Thermal-chainbranching model for the explosion peninsula (in the Press).Google Scholar
(5)Golubitsky, M. and Schaeffer, D.A theory for imperfect bifurcation via singularity theory. Commun. Pure Appl. Math. 32 (1979), 21–98.CrossRefGoogle Scholar
(6)Golubitsky, M. and Schaeffer, D.Imperfect bifurcation in the presence of symmetry. Commun. Math. Phys. 67 (1979), 205–232.CrossRefGoogle Scholar
(7)Gray, B. F.Theory of branching reactions with chain interaction. Trans. Faraday Soc. 66 (1970), 1118–1126.CrossRefGoogle Scholar
(8)Gray, B. F. and Yang, C. H.On the unification of the thermal and chain theories of explosion limits. J. Phys. Chem. 69 (1965) 2747.CrossRefGoogle Scholar
(9)Poston, T. and Stewart, I. N.Catastrophe Theory and its Applications (Pitman, London and Boston, 1978).Google Scholar
(10)Thom, R.Structural Stability and Morphogenesis (translation, Fowler, D. H.), (Benjamin, Reading Mass. 1975).Google Scholar