  The evolution of two-component cold atoms on a ring with quasispin-orbit
(qSO) coupling and spin-flip has been studied analytically (for arbitrary
particle number $ N $ without interaction) and numerically (for a few-body
system with interaction). Counter-propagating and oscillating persistent
spin-currents have been found. The regularity governing the period and
amplitude of oscillation has been clarified. When the strengths for the qSO
coupling and spin-flip are fixed, the frequency of oscillation can be
effectively tuned by the Raman detuning, while the amplitude can be tuned by
either changing the initial status and/or the Raman detuning. When the initial
numbers of atoms of the two-components $N_{1}$ and $N_{2}$ are close to each
other, the oscillation will be seriously suppressed. The condition for
maximizing the amplitude of oscillation is given.
