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The seven elementary catastrophes

Catastrophes in systems with two state variables:

The hyperbolic umbilic

Germ

Unfolding

An applet

The hyperbolic umbilic properties will be studied by means of this applet.

Bottom : Control panel. The hyperbolic umbilic has three control parameters;

Left : space control representation, control parameters values and bifurcation set on a plane (a = A value) through the three dimensional control space.

Middle : surface of potential as a "geographical map". Grey levels convey information about the potential value, coordinates on the plane are state variable values. Darkest greys are minimums.

Right : state variables equilibrium values on a two-dimensional color scale
Stability of state variable equilibrium may be tested by clicking on a potential map point.

Bifurcation set

Hyperbolic umbilic germ may be thought as the collapse of one minimum, one maximum and two saddles.

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