Explore 1D and 2D bifurcations: saddle-node, transcritical, pitchfork, Hopf. Phase portraits and bifurcation diagrams. Watch fixed points appear, collide, and exchange stability.
Bifurcation theory (Poincaré, Andronov, Hopf): topological changes in flow as parameter varies. Codimension-1 bifurcations are generic (saddle-node, Hopf). Center manifold theorem: high-dim dynamics near bifurcation reduce to 1 or 2 normal form equations.