The intermediate mode between the ohmic, or low confinement (L-mode), and the increased confinement (H-mode) regimes, or the so called I-phase, which is characterized by the existence of zonal flows in the form of limit cycle oscillations (LCOs), was observed on the Globus-M tokamak. Depending on the LCO frequency, the I-phase resulted in either a transition to H-mode or back to L-mode. The possibility of L-I-H transition initiation induced by LCOs and the effect of LCO frequency were studied by means of numerical modeling of the density profile evolution, taking into account turbulence suppression by the inhomogeneous radial electric field. The modeling results show that lower LCO frequency could be a factor facilitating the L-H transition, whereas higher frequency LCOs are more likely to cause the backward transition to L-mode. The results are in qualitative agreement with the results of the studies of geodesic acoustic mode (GAM)–initiated L-H transition in the TUMAN-3M tokamak, where a lower GAM frequency was found to be beneficial for L-H transition initiation.