Assess graduate-level ability to analyze stability and bifurcation structures in reaction–diffusion models of biological pattern formation: derive and interpret dispersion relations for two-component systems, state and verify Turing instability criteria, perform weakly nonlinear (amplitude-equation) analysis to show how nonlinear saturation selects finite-amplitude patterns, interpret bifurcation diagrams including codimension-1/2 transitions, and evaluate parameter sensitivity (diffusion ratios, kinetics, domain size) using continuation and simple numerical examples.