Abstract
The predictions of many scientific models are highly sensitive to small perturbations of the equations. Topological study of these can clarify and improve robustness of the models, sometimes revealing new phenomena implicitly associated with them.
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Bibliography
D.R.J. Chillingworth, Differential Topology with a View to Applications, Research Notes in Math. 9, Pitman, London 1976.
M.A. Golubitsky and D.G. Schaeffer, A Theory for Imperfect Bifurcation via Singularity Theory, Comm. Pure & Appl. Math., XXXII (1979), 21–98.
M.A. Golubitsky and D.G. Schaeffer, Imperfect Bifurcation in the Presence of Symmetry, preprint, CUNY, 1978.
M.W. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, New York 1974.
B. Malgrange, The preparation theorem for differentiate functions, in Differential Analysis, Bombay Colloquium, Oxford University Press, Oxford and New York 1964, pp 203–208.
J. Palis and S. Smale, Structural Stability Theorems, in Global Analysis, Proc. Symp. Pure Math. 14, Am. Math. Soc., Providence, Rhode Island, 1970, pp 223–231.
T. Poston and I.N. Stewart, Catastrophe Theory and its Applications, Pitman, London & California 1978.
D.G. Schaeffer and M.A. Golubitsky, Bifurcation Analysis near a Double Eigenvalue of a Model Chemical Reaction, MRC Technical Summary Report 1859, Math. Research Ctr, University of Wisconsin 1978.
R. Thom, Stabilité Structurelle et Morphogénèse, Benjamin, New York, 1972. Translated D.H. Fowler as Structural Stability and Morphogenesis, Benjamin-Addison Wesley 1975.
E.C. Zeeman, Catastrophe Theory-Selected Papers 1972–1977, Addison-Wesley, 1977.
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© 1980 Springer-Verlag Berlin Heidelberg
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Poston, T. (1980). Structural Instability in Systems Modelling. In: Haken, H. (eds) Dynamics of Synergetic Systems. Springer Series in Synergetics, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67592-8_20
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DOI: https://doi.org/10.1007/978-3-642-67592-8_20
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