Search Results for ""

For any system that seeks to minimize a function, only seven different local forms of catastrophe "typically" occur for four or fewer variables: 1. Fold catastrophe, 2. Cusp ...

Catastrophe theory studies how the qualitative nature of equation solutions depends on the parameters that appear in the equations. Subspecializations include bifurcation ...

A theory is a set of sentences which is closed under logical implication. That is, given any subset of sentences {s_1,s_2,...} in the theory, if sentence r is a logical ...

A catastrophe which can occur for one control factor and one behavior axis. It is the universal unfolding of the singularity f(x)=x^3 and has the equation F(x,u)=x^3+ux.

A catastrophe which can occur for three control factors and two behavior axes. The elliptical umbilic is catastrophe of codimension 3 that has the equation ...

A catastrophe which can occur for three control factors and two behavior axes. The hyperbolic umbilic is the universal unfolding of the function germ f(x,y)=x^3+y^3. The ...

A catastrophe which can occur for four control factors and two behavior axes. The parabolic umbilic catastrophe is given by the unfolding ...

A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...

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 ...

A cusp catastrophe is a catastrophe which can occur for two control factors and one behavior axis. The cusp catastrophe is the universal unfolding of the singularity f(x)=x^4 ...