A circular superconductor with a weak-link junction is considered in the pr
esence of a dc voltage bias. Using a time-dependent perturbed method, we ob
tain a unitary evolution operator or the driven SQUID system. We investigat
e the step structure of the screening current in the system and show that,
due to the Josephson nonlinear term, the Aux and charge can exhibit reduced
quantum fluctuation behavior.