Two-parameter bifurcation diagram of ẋ = μx − x³ + αy, ẏ = νy − x² (Bogdanov-Takens normal form). Click anywhere on the left panel to set (μ, ν) and watch the phase portrait.
Codimension-2 Bogdanov-Takens point: Hopf curve (oscillation birth), saddle-node curve (fixed points collide), and homoclinic orbit curve all meet at a single point in parameter space.