Normal Form Bifurcations

Center manifold reduction & universal unfoldings of codimension-1/2 bifurcations


Bifurcation Type

Normal Forms

ẋ = μ + x² (saddle-node)
Fixed pts: ẋ=0 — solid=stable, dashed=unstable
Center manifold: reduces dim near bifurcation
Codim-k: k params needed to unfold generically

Phase Portrait

2D vector field. Trajectories shown for current μ,ν.