  In the context of a spatially extended model for the electrical activity in a
pituitary lactotroph cell line, we establish that two delayed bifurcation
phenomena from ODEs ---folded node canards and slow passage through Hopf
bifurcations--- persist in the presence of diffusion. For canards, the single
cell (ODE) model exhibits canard-induced bursting. Numerical simulations of the
PDE reveal rich spatio-temporal canard dynamics, and the transitions between
different bursts are mediated by spatio-temporal maximal canards. The ODE model
also exhibits delayed loss of stability due to slow passage through Hopf
bifurcations. Numerical simulations of the PDE reveal that this delayed
stability loss persists in the presence of diffusion. To quantify and predict
the delayed loss of stability, we show that the Complex Ginzburg-Landau
equation exhibits the same property, and derive a formula for the space-time
boundary that acts as a buffer curve beyond which the delayed onset of
oscillations must occur.
