Multiparameter Parallel Search Branch Switching

A continuation method (sometimes called path following) is a way to compute solution curves of a nonlinear system of equations with a parameter. We derive a simple algorithm for branch switching at bifurcation points for multiple parameter continuation, where surfaces bifurcate along singular curves on a surface. It is a generalization of the parallel search technique used in the continuation code AUTO, and avoids the need for second derivatives and a full analysis of the bifurcation point.