Bifurcation Normal Forms — Codimension-2
Cusp, Bogdanov-Takens, Bautin (degenerate Hopf) · Phase portraits & unfoldings
Normal form
Cusp catastrophe
Bogdanov-Takens
Bautin (degen. Hopf)
Parameter μ₁
0.00
Parameter μ₂
0.00
Phase speed
1.0
Pause
Reset trajectories
Cusp: ẋ = μ₁ + μ₂x − x³. Fold curves: μ₁ = ±(2/3)(−μ₂/3)^(3/2) (when μ₂<0). Codimension-2 point at origin where fold merges.