Singular analysis of two-dimensional bifurcation system (Q987293)

The two-dimensional system \((x^{2}-y^{2}-\lambda,y^{2}-\lambda)\) is considered. Universal unfolding and transition sets of the bifurcation equations are obtained. It is demonstrated that the system has lost many bifurcation properties when it is reduced to a one-dimensional one \(g=x^{2}-2 \lambda\).