Slow spectral dynamics of shot noise in the Kuramoto model: The role of microscopic regularity

Finite-size effects in the Kuramoto model are known to induce collective fluctuations even below the critical coupling, where the thermodynamic limit predicts complete asynchrony. While the shot-noise approach developed in our recent work has been shown to accurately capture the power spectrum of these fluctuations for random frequency sampling, we here demonstrate that the features of the fluctuations' power spectrum crucially depend on the frequency sampling method. We show that a deterministic (quasi-uniform) selection of natural frequencies from the same Lorentzian distribution leads to qualitatively different dynamics: the shot-noise spectrum exhibits anomalously slow oscillatory behavior, manifesting as wave-like patterns in time-frequency representations. The period of these oscillations scales linearly with the system size and matches the frequency spacing between neighboring oscillators near the distribution center. Numerical simulations confirm that these slow spectral dynamics arise from resonant interactions facilitated by the regular frequency structure, which are absent for random sampling. Our findings demonstrate that identical integral frequency distributions do not guarantee equivalent collective dynamics, highlighting the necessity of accounting for the fine structure of microscopic parameters in finite-size populations.