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Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators
Fig 2
The antagonistic effect of IEDs on the transition to seizure.
Panels A and B show, in red, the v-nullcline whose stable branches correspond to the stable low and high activity states of the system. The unstable part of the v-nullcline (dashed red line) separates the basin of attraction of both branches. As was illustrated in [22], Figure 5, whether the pulses make the system cross the unstable part of the v-nullcline determines the opposite nature of IEDs. For a random train with amplitude A = 0.25 and 
the system goes to seizure (panel A). By contrast, for a random train with amplitude A = 0.5 and 
the system avoids the seizure state (panel B). By plotting the change in seizure rate Δ as a function of both the amplitude, A, and the mean inter-perturbation interval, Ts (panel C), we can distinguish between pro-convulsive regimes (yellow and white areas) in which the transition is potentiated, and preventive regimes (red and black areas) in which the transition is delayed or completely suppressed. We refer the reader to Materials and Methods section for the specific details about the computation of panel C.
doi: https://doi.org/10.1371/journal.pcbi.1008521.g002