  The stability of cortical function depends critically on proper regulation.
Under conditions of migraine and stroke a breakdown of transmembrane chemical
gradients can spread through cortical tissue. A concomitant component of this
emergent spatio-temporal pattern is a depolarization of cells detected as slow
voltage variations. The velocity of ~3 mm/min indicates a contribution of
diffusion. We propose a mechanism for spreading depolarizations (SD) that rests
upon a nonlocal or non-instantaneous feedback in a reaction-diffusion system.
Depending upon the characteristic space and time scales of the feedback, the
propagation of cortical SD can be suppressed by shifting the bifurcation line,
which separates the parameter regime of pulse propagation from the regime where
a local disturbance dies out. The optimisation of this feedback is elaborated
for different control schemes and ranges of control parameters.
