The researchers studied how adding noise to a nonchaotic logistic map affects synchronization time. They found that as noise intensity increases, the Lyapunov exponent changes from negative to positive. When the Lyapunov exponent is negative, orbits with different starting points sync up. However, when noise intensity is high, synchronization time is not solely determined by the Lyapunov exponent. The reduction in synchronization time is due to initial nonstationary behaviors, with the critical point of the logistic map being crucial.