Before revision:  We find that the existence of the period  mismatch induces an enhancement of entrainment in both smooth and relaxation oscillators. By calculating Floquet multipliers, we show that the enhancement mechanism is based on the coupled oscillators which are in the vicinity of  bifurcation on limit cycle  .
After revision:  We find that the existence of the period mismatch induces an enhancement of entrainment in both oscillators; the enhancement occurred in the vicinity of bifurcation on limit cycle .