Before revision:  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:  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 . The optimal period ratio in the smooth oscillator for the enhanced trainability coincided with the experimentally observed ratio, which suggested the biological exploitation of the period mismatch. Although the origin of multiple feedback loops is often accounted for by the notion of passive robustness against perturbation, we here studied active benefits of the period mismatch on the efficiency of genetic oscillators. Our findings show qualitatively different perspective on the essentiality and inherent advantage of multiple loops in genetic oscillators .