Comparison of the Fold and Cusp Catastrophe Models for Tensile Cracking and Sliding Rockburst

Table 1

Standard forms of the seven elementary catastrophe models.

Catastrophe model	Dimension of control parameters	Dimension of state variables	Expression of the potential function	Equilibrium surface M	Singular point set S
Fold	1	1
Cusp	2	1
Swallowtail	3	1
Butterfly	4	1
Elliptic umbilicus	3	2
Hyperbolic umbilicus	3	2
Parabolic umbilicus	4	2