Assess graduate-level competence in linear and nonlinear stability analysis and bifurcation structure of reaction–diffusion models for biological pattern formation, including derivation and interpretation of dispersion relations, identification of Turing and Turing–Hopf instabilities, classification of bifurcations (super/subcritical), weakly nonlinear amplitude equations, effects of domain size and boundary conditions, and use of numerical continuation and eigenvalue tracking to construct and interpret bifurcation diagrams in biological contexts.