Assess graduate-level ability to analyze stability, bifurcations, and spatial pattern formation in reaction–diffusion models of biological morphogenesis. Topics include linear stability and dispersion relations for homogeneous steady states, criteria for Turing and Hopf instabilities, weakly nonlinear amplitude equations and pattern selection, parameter-dependent bifurcation structure (Turing, Hopf, Turing–Hopf), effects of domain size and boundaries, and numerical continuation/eigenvalue methods to determine pattern stability.