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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.

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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

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