Before revision:  The entrainment is calculated with a phase reduction approach and a Floquet multiplier analysis, and their dependencies on coupling strength and the period ratio are investigated in two genetic oscillator models (smooth and relaxation oscillators). We find that the existence of the period  mismatch induces an enhancement of entrainment in both smooth and relaxation oscillators.
After revision:  The entrainment is calculated with a phase reduction approach and a Floquet multiplier analysis, and their dependencies on coupling strength and period mismatch induces an enhancement of entrainment in both smooth and relaxation oscillators.