Assess graduate students' ability to analyze equilibria, local stability, and bifurcations in nonlinear ecological models (e.g., Lotka–Volterra predator–prey, Rosenzweig–MacArthur, and competing species systems). Tasks include finding equilibria, computing Jacobians and eigenvalues, classifying stability, sketching nullclines and phase portraits, identifying saddle-node, transcritical, and Hopf bifurcations as parameters vary, constructing simple bifurcation diagrams, and interpreting ecological consequences such as persistence, oscillations, or extinction. Problems may require analytic derivations and qualitative/numerical phase-plane reasoning.