  We study the dynamic behaviour of a quantum two-level system with
periodically varying parameters by solving the master equation for the density
matrix. Two limiting cases are considered: multiphoton Rabi oscillations and
Landau-Zener transitions. The approach is applied to the description of the
dynamics of superconducting qubits. In particular, the case of the
interferometer-type charge qubit with periodically varying parameters (gate
voltage or magnetic flux) is investigated. The time-averaged energy level
populations are calculated as funtions of the qubit's control parameters.
