Graphical model showing how a tipping point for cortical spreading depression can arise.

<p>a) Three equilibriums may occur at intersection points where the rate of generation of new pulses (sigmoidal curve) equals the rate of decay (dashed line) of neural pulses. Activity increases when the generation of new pulses exceeds the decay of pulses (sections I and III) and decreases in the other sections (sections II and IV). It can be seen from the arrows representing this direction of change that the middle intersection point is a repellor that marks the border between the basins of attraction of the two alternative stable states. b) Increasing base-line excitability promotes the generation of new pulses causing the unstable equilibrium (open dot) and the stable normal state (left hand solid dot) to move closer together. This reduces resilience of the normal state in the sense that a smaller perturbation is needed to invoke a shift to the Aura state (horizontal dashed arrows in panel). c) Plotting how the intersection points representing equilibriums move as a function of base-line excitability, a catastrophe fold arises. The fold bifurcation point (F) marks the loss of stability of the normal state.