PARAMETER SPACE (μ₁, μ₂) — Click to select point
PHASE PORTRAIT (x, y)
μ₁ = –, μ₂ = –
Saddle-node curve
Hopf curve
Homoclinic curve
BT point (origin)
Bogdanov-Takens is the codimension-2 bifurcation where a double-zero eigenvalue occurs. The 2D unfolding produces three curves meeting at the BT point: saddle-node (SN): μ₁ = 0, Hopf (H): μ₁ = −μ₂²/4, and a homoclinic (HC) curve tangent to H. This is one of the most complete local bifurcation analyses possible — the full global dynamics unfolds from a single degenerate point.