[ToC]

 

P. T. Saunders, An Introduction to Catastrophe Theory, Cambridge U. Press, 1980

CROSS SECTIONS OF THE BIFURCATION SET OF THE BUTTERFLY FOR DIFFERENT VALUES OF U ANDT

These results are easily established by arguments exactly similar to those we employed when discussing the swallowtail catastrophe. We can deal with the two remaining regions without performing any calculations by remarking that when we cross the bifurcation set of a cuspoid, then in general (by which we mean if we do not cross it at a special point such as a point of self-intersection) we either add or subtract a pair of equilibria, one stable and one unstable.