Assess learners' ability to analyze local stability and detect/characterize bifurcations in finite-dimensional nonlinear dynamical systems using center manifold reduction and normal form calculations. Tasks include deriving reduced dynamics near nonhyperbolic equilibria, computing normal form coefficients to classify saddle-node, transcritical, pitchfork, and Hopf bifurcations, and interpreting stability, bifurcation type, and unfolding parameters for applied problems.