attractors are presented in Fig. 8, the left column shows the SPS of the attracting processes, the right column shows the phase trajectories and SPS of the final states, (A) and (B) for $\Delta
E_{1}=3.000$, (C) and (D) for $\Delta E_{1}=7.500$. In the SPS, after the transient chaos, the sampled points gradually come to the final fixed points. The phase trajectories of final oscillations are closed curves, and the corresponding SPS only contain fixed points which are noted as small circles, so the final oscillations are frequency-locked (FL). When $\Delta
E_{1}=3.000$, there is only a single fixed point in the SPS, the corresponding final oscillation is a period-one limit-cycle with frequency $%
\omega $; while for $\Delta E_{1}=7.500$, there exist five fixed points, and then the final oscillation is a $\frac{1}{5}$ FL motion, this means the oscillating frequency is $\frac{1}{5}\omega $. Fig. 9 presents the similar dynamics starting form MQST, with $z(0)=0.75$, $\phi (0)=0.0$, $\Delta
E_{0}=0.0$, $\Lambda =10.0$, $\omega =2\pi $ and $\eta =0.001$, for different parameter $\Delta E_{1}$. Where, (A) and (B) for $\Delta
E_{1}=1.000$, (C) and (D) for $\Delta E_{1}=1.700$. The transient chaos and the FL oscillations appear too. When $\Delta E_{1}=1.000$, the eventual oscillation is a period-one 