Neural mass modeling of slow-fast dynamics of seizure initiation and abortion

The paper correctly identifies, via slow–fast geometric analysis and simulations, that biphasic stimulation can abort pre‑ictal bursting, that exciting SOM+ is the most effective target, and that higher frequency is needed when all subpopulations are stimulated; however, it stops short of a rigorous theorem (it argues with constant-input geometry and then demonstrates numerically) . The model’s solution gives a plausible averaging/Fenichel-based route to a proof and explains the threshold ordering, but it omits key conditions (e.g., amplitude constraints to remain in the convex region of S, quantified averaging error bounds in the three–timescale setting, and explicit margins relative to the Hopf window). Hence both are substantively correct in intuition but incomplete as rigorous arguments.