The Computation of Symmetry-Breaking Bifurcation Points
Bodo Werner, Alastair A. Spence · SIAM Journal on Numerical Analysis · 1984
We consider symmetry-breaking simple singular points of a parameter dependent nonlinear equation $g(\lambda ,x) = 0$. Such points are intimately connected to pitchfork bifurcation points, and we show that they can be computed in a stable way using a suitable extended system. Because of the underlying symmetry this system is much simpler than other extended systems for the computation of secondary bifurcation points.