cusp (version 2.3.8)

cusp.extrema: Locate Extrema of Cusp Catastrophe Potential Function

Description

This function computes the locations of the extrema of the cusp catastrophe potential function.

Usage

cusp.extrema(alpha, beta)

Value

Ordered vector with locations of extremes.

Arguments

alpha

(single) value of normal/symmetry factor

beta

(single) value of bifurcation/splitting factor

Author

Raoul Grasman

Details

The locations are determined by computing the solutions to the equation $$\alpha+\beta\,X - X^3 = 0.$$

References

http://www.scholarpedia.org/article/Cusp_bifurcation

See Also

cusp.bifset

Examples

    # simple use
    cusp.extrema(2,3)
    
    # using vectorize to allow for array input; 
    # returns a matrix with locations in each column
    Vectorize(cusp.extrema)(-3:3, 2)