Assess graduate-level ability to analyze stability and bifurcation in nonlinear reaction–diffusion systems relevant to biological pattern formation. Scope includes deriving dispersion relations and Turing instability criteria, solving the linear eigenvalue problem on bounded domains with various boundary conditions, classifying local bifurcations (pitchfork, Hopf, saddle-node), performing weakly nonlinear (amplitude/Ginzburg–Landau) reductions, and using numerical continuation to track solution branches; interpret results for activator–inhibitor models and discuss parameter and domain effects.