Numerical methods for steady-state mode interactions

Mock interactions on nontrivial solutions for problems withZ₂ x Z₂ symmetry are considered. It is assumed that a path ofbifurcation points is being followed with two parameters anda mode interaction then corresponds to two separate bifurcationsof an extended system. This view of mode interactions leadsto efficient numerical methods for dealing with such pointsand for swapping onto the new paths of bifurcation points whichoriginate them. The nondegeneracy conditions associated withmode interactions are also interpreted in this context.