Structural Instability in Systems Modelling

  • T. Poston
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 6)


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.


Catastrophe Theory Small Term Frontier Point Pure Imaginary Eigenvalue Asymmetric Perturbation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D.R.J. Chillingworth, Differential Topology with a View to Applications, Research Notes in Math. 9, Pitman, London 1976.MATHGoogle Scholar
  2. 2.
    M.A. Golubitsky and D.G. Schaeffer, A Theory for Imperfect Bifurcation via Singularity Theory, Comm. Pure & Appl. Math., XXXII (1979), 21–98.CrossRefMathSciNetGoogle Scholar
  3. 3.
    M.A. Golubitsky and D.G. Schaeffer, Imperfect Bifurcation in the Presence of Symmetry, preprint, CUNY, 1978.Google Scholar
  4. 4.
    M.W. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, New York 1974.MATHGoogle Scholar
  5. 5.
    B. Malgrange, The preparation theorem for differentiate functions, in Differential Analysis, Bombay Colloquium, Oxford University Press, Oxford and New York 1964, pp 203–208.Google Scholar
  6. 6.
    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.Google Scholar
  7. 7.
    T. Poston and I.N. Stewart, Catastrophe Theory and its Applications, Pitman, London & California 1978.MATHGoogle Scholar
  8. 8.
    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.Google Scholar
  9. 9.
    R. Thom, Stabilité Structurelle et Morphogénèse, Benjamin, New York, 1972. Translated D.H. Fowler as Structural Stability and Morphogenesis, Benjamin-Addison Wesley 1975.Google Scholar
  10. 10.
    E.C. Zeeman, Catastrophe Theory-Selected Papers 1972–1977, Addison-Wesley, 1977.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • T. Poston
    • 1
  1. 1.Département de Physique ThéoriqueUniversité de GenèveGenève 4Switzerland

Personalised recommendations