Assess students' ability to detect and classify local bifurcations (saddle-node, transcritical, pitchfork, Hopf) in one-parameter planar ODE families by linearizing at equilibria, computing eigenvalues, performing center-manifold reduction when necessary, deriving normal forms and leading-order unfolding coefficients, verifying nondegeneracy and transversality conditions, and sketching local phase portraits and bifurcation diagrams; tasks include symbolic computation, justification of reductions, and interpretation of resulting dynamics.