<p>To investigate the effects of non-uniform medium perturbations on detonation propagation in annular channels, this study employs the Euler equations coupled with a two-step induction-reaction kinetics model. A stoichiometric hydrogen-air mixture is used, in which a sinusoidal density perturbation is introduced, with its amplitude and frequency systematically varied. The results show that such non-uniform perturbations can induce localized decoupling and re-initiation processes at the detonation front. The amplitude of the perturbation determines the magnitude of local density and temperature gradients; larger amplitudes enhance the suppression of transverse waves, thereby increasing the instability of detonation propagation. Under large-amplitude perturbations, the detonation wave exhibits markedly different responses to perturbation frequency. Low-frequency perturbations tend to trigger periodic decoupling and re-initiation, while high-frequency perturbations lead to extensive wavefront decoupling. Further analysis of the flow structures and wall pressure distributions reveals that, under low-frequency conditions, the coupling between density gradients and inner-wall diffraction promotes the formation of strong transverse waves. In contrast, high-frequency perturbations impose rapid thermodynamic variations that the detonation wave cannot effectively respond to, suppressing the development of transverse structures and preventing the formation of strong transverse waves.</p>