A narrow-bandwidth resonance-gated Kuramoto model of individualized gamma entrainment

Objective. We examined whether frequency mismatch between fixed 40 Hz Gamma ENtrainment Using Sensory Stimulation (GENUS) and an assigned local resonance centre reduces simulated entrainment, and what this implies for individualized stimulation. Approach. A forced Kuramoto population received stimulation through an assumed Gaussian resonance gate. Unforced and ungated controls separated gate effects from oscillator dynamics. We tested bandwidth (BW), coupling, amplitude, gate shape, swept stimulation and a delayed modular network. BW denotes the input gate's standard deviation. Existing event-related synchronization (ERS) and within-visual connectivity-strength data were analyzed with separate observation templates. Main results. Predictions were conditional on the imposed gate. At BW=0.5 Hz, a 2 Hz mismatch reduced stimulus-referenced phase-locking value (PLV_stim) by 95.0%, from 0.508 to 0.026. At BW=2–3 Hz, reductions were 31.0–46.9% at default coupling and 29.9–51.9% across couplings. Narrow-gate attenuation persisted under tested supercritical coupling. Compensation depended on gate tails and amplitude; finite Gaussian gain permitted compensation at sufficiently large internal drive. Among 200 simulated subjects, matched stimulation yielded 13.71-fold higher PLV_stim than fixed 40 Hz. Sweeps produced transient resonance capture with little subsequent locking. In the delayed network, collective frequencies fell below nodal frequencies, while raw selectivity depended on gate placement and unforced reference locking. Empirical ERS and connectivity strength did not uniquely identify physiological gate BW or validate 0.5 Hz. Significance. The model quantifies consequences of a narrow-gate hypothesis rather than establishing narrow biological tuning. Results motivate measuring individual stimulation–response curves, including network outcomes, but do not establish an optimal individualized GENUS protocol or support frequency prescription from a resting gamma peak alone.