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Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators
Fig 10
Response of perturbations for the reduced epileptor (29).
We show the change in the seizure rate Δ for a random train of pulses whose mean inter impulse interval follows a normal distribution 
with a mean time Ts and standard deviation σ. Panels A, B, C correspond to the sets of parameters 
and 
in Table 1. Left Figures correspond to the periodic case 
and right Figures to the random case 
. Consistently with our theoretical analysis there is a direct correspondence between the mean distance between the lower branch and the slow nullcline and the minimal pulse amplitude A for which perturbations may lead to lock the system. Purple solid lines, bounding locking regimes, correspond to the bifurcations of the map (25). By drawing the same curve for the random case, we illustrate the resilience of locking states to noise. For the specific details about the numerical computation of this Figure, we refer the reader to Materials and Methods section.
doi: https://doi.org/10.1371/journal.pcbi.1008521.g010