common phenomenon in these dynamical systems is that they seem to behave chaotically during some transient periods, but eventually fall onto periodic stable attractors. This has been called as the transient chaos or chaotic transient. Superlong transient chaos occurs commonly in dissipative dynamical system, in this case, oscillations starting from random initial conditions oscillate chaotically for a very long time before they set into the final attractors which are usually regular and stable \[22,23\]. In our system, we also find the transient chaos and final attractors. Using the SPS of $(z,dz/dt)$, we exhibit the attracting process of the transient chaos and the fixed points of the final attractors. The phase trajectories of the final attractors are also showed.

For a certain damping parameter $\eta $, and fixed value of parameter $%
\Lambda $, $\Delta E_{0}$, there exist many types of attractors when $\Delta
E_{1}$ is changed. For the same $\Delta E_{1}$, different initial conditions will lead different final states. Starting from Rabi oscillation, with $%
z(0)=0.5$, $\phi (0)=0.0$, $\Delta E_{0}=0.0$, $\Lambda =10.0$, $\omega
=4\pi $ and $\eta =0.01$, for different parameter $\Delta E_{1}$, the SPS of the attracting processes and the final attractors, and the phase trajectories of the final 