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Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators

Fig 6

PRC of pulses A > 0 for relaxation oscillators.

Next we sketch the PRCs for pulses of amplitude A > 0 for the case . For phases θ < θ*, where θ* satisfies , due to the slope of isochrons the effect of the pulses will be to delay trajectories. Since isochrons approach the unstable point P through , the closer the phase θ to θ*, the larger the bending of the isochrons and thus the larger the corresponding delay value. For phases , there is an advancement proportional to the fraction of cycle skipped. This prevalence of advancements is also seen for points in the upper branch. For phases in a neighbourhood of the fold point , we expect a transition between advancement and delays not drawn because our analysis is only valid for normally hyperbolic points.

doi: https://doi.org/10.1371/journal.pcbi.1008521.g006