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CATASTROPHE TEACHER

an introduction for experimentalists

 

The seven elementary catastrophes

| the fold |  the cusp |  the swallowtail |  the butterfly |  the hyperbolic umbilic |  the elliptic umbilic |  the parabolic umbilic |

Catastrophes in systems with only one state variable:

The fold catastrophe

Germ

V = x3

Unfolding

V(a) = x3 - ax

An applet

The fold catastrophe properties will be studied by means of this applet

  • Bottom : Control panel. The fold catastrophe has only one control parameter
  • Left : space control representation, control parameter values and bifurcation set
  • Right : state variable versus potential value; below, state variable equilibrium value on a color scale
    Stability of state variable equilibrium may be tested by clicking on a potential curve point.

    • Bifurcation set

    The control space is one-dimensional; bifurcation set is made of only one point. The fold catastrophe is similar as the "all or none" law; its bifurcation set is the all or none threshold.

    | the fold |  the cusp |  the swallowtail |  the butterfly |  the hyperbolic umbilic |  the elliptic umbilic |  the parabolic umbilic |

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    Author: Lucien Dujardin

    Faculté de Pharmacie BP 83 F 59006 Lille Cedex France

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