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Catastrophe theory was introduced in the late 1960's by René Thom, but his book "Stabilité structurelle et morphogenèse" was only published in 1972. An english translation by David Fowler has been available since 1975. (Thom R. - Structural stability and morphogenesis. Benjamin Addison Wesley, New York, 1975.)

Thom's ideas were then developed by E.C. Zeeman who proposed many applications in various domains. (see Zeeman E. C. - Catastrophe theory, selected papers. Addison-Wesley publishing compagny, London, 1977.)

Catastrophe?

• What is this, in Catastrophe theory
• An applet to experiment with catastrophes

• This applet as a black box: how to interpret its behaviour ?
• The cusp as a model for the applet behaviour
  • State variable, command space, potential, Maxwell or delay law, equilibrium manifold
• Explore other cusp properties by means of the applet
  • Hysteresis
  • Divergence
  • Inaccessibility
• Some other catastrophe machines for a more precise exploration of the stability notion
  • Zeeman's catastrophe machine
    • Zeeman's catastrophe machine as an applet
  • The gravitational catastrophe machine (JMT Thompson)
    • The gravitational catastrophe machine as an applet
  • Stability and perturbation
    • Perturbation of control parameters and structural stability
    • Perturbation of state variable and position stability

• Catastrophes in systems with only one state variable:
  • The fold
  • The cusp
  • The swallowtail
  • The butterfly
• Catastrophes in systems with two state variables
  • The hyperbolic umbilic
  • The elliptic umbilic
  • The parabolic umbilic

Links about Catastrophe theory

• Catastrophe theory : a lecture by E.C. Zeeman, Trinity University, San Antonio, March, 1995 (for any people)
• Chaos and Catastrophes : a lecture by E.C. Zeeman, Research Conference in Dynamics #1, Boston University, June 30 - July 3, 1991 (for mathematicians)
• Microbial Ecology : Catastrophe Theory and Chaos Theory in Microbiology
• grasshopper infestations : The Catastrophe Theory Model is a model which predicts grasshopper infestations based on climatic data (mean daily temperature and three month precipitation accumulations) and historic site specific information relevant to grasshopper population preferences. The model uses catastrophe theory to predict grasshopper infestations based on the grasshopper infestation level in the previous year and the weather data for the current year.
• Multiple Stable States: The complex Dynamics of succession.
• Candida albicans morphogenesis : ... So, chlamydospore production seems to be an "all or nothing" phenomenon, a complicated one: several parameters control it at the same time; they have to cross a threshold; this control threshold is a multidimensional one. Morphogenesis links environmental continuous change with the sudden changes in shape expressed by Candida albicans. Catastrophe theory proposes a framework to describe such phenomena.
• Web Dictionary of Cybernetics and Systems :
  basin, behavior, behavior space, bifurcation, black box method, catastrophe theory, control, creod, equilibrium states vs transient states, equilibrium, linear, multistable system, stability, system.

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  Auteur: Lucien Dujardin

  Faculté de Pharmacie BP 83 F 59006 Lille Cedex France

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