Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators
Fig 7
Mechanism preventing the emergence of seizures.
To suppress the original oscillation and keep the system in the lower branch of Γϵ the amplitude A of the pulse has to be large enough so besides causing a delay Δθ, it displaces trajectories above enough the slow-nullcline so the distance travelled in the negative direction overcomes the distance travelled in the positive direction, thus causing a negative net displacement. The locking appears by repeating this mechanism after Ts = TΔθ intervals so the new pulse always hits the system at the same initial point.