Bifurcation hierarchy of symmetric structures

A group-theoretic method for the analysis of bifurcation behavior of regular-polygonal symmetric structures is described. Possible bifurcation paths and points of these structures are categorized in terms of dihedral and cyclic groups, which express the symmetry. In particular, we offer a complete description of those double bifurcation points which occur due to group symmetry. The type, the number, and the stability of bifurcation paths branching at these points are determined by deriving bifurcation equations. The existence of a potential function plays a substantial role for the existence of bifurcation paths. As a result of these, all possible bifurcation process can be known a Priori as a natural consequence of bifurcation hierarchy before actual numerical analysis. An implementation of this method in numerical analysis shows its validity and usability.