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Butterfly Catastrophe

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ButterflyCatastrophe

A butterfly catastrophe is a catastrophe which can occur for four control factors and one behavior axis. The butterfly catastrophe is the universal unfolding of the singularity f(x)=x^6 of codimension 4, i.e., with four unfolding parameters. It has the form F(x,u,v,w,t)=x^6+ux^4+vx^3+wx^2+tx.

ButterflyCatastrophe2D

The equations

x=c(8at^3+24t^5)
(1)
y=c(-6at^2-15t^4)
(2)

display such a catastrophe (von Seggern 1993).

See also

Butterfly Curve, Butterfly Effect, Butterfly Function, Butterfly Graph, Butterfly Lemma, Butterfly Polyiamond, Butterfly Theorem

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References

Sanns, W. Catastrophe Theory with Mathematica: A Geometric Approach. Germany: DAV, 2000.von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 94, 1993.

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Butterfly Catastrophe

Cite this as:

Weisstein, Eric W. "Butterfly Catastrophe." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ButterflyCatastrophe.html

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