Bifurcation Normal Forms

Saddle-node, transcritical, pitchfork, Hopf — interactive bifurcation explorer

Parameter μ: 0.00 Higher-order a: 1.00

ẋ = μ + x²

— Stable branch
— Unstable branch
● Equilibrium (current μ)

Saddle-node: two fixed points
annihilate as μ → 0.
Generic codimension-1 bif.
Exists when: ẋ=0, ∂ẋ/∂x=0.