An analytical solution of the master equation that describes two charge superconducting
qubits interacts with a single microwave cavity field mode within dispersive
approximation and dissipation region of the qubit damping. Quantum correlations of
a general two-qubit state (non-X-state) are studied by using three different quantum
correlation quantifiers: measurement-induced non-locality, geometric quantum discord
and logarithmic negativity. It is shown that the quantum correlations are sensitive
to the choice of the parameters of the qubit dissipation rate, coherent state intensity
and the initial qubit distribution angle. The generated oscillatory behavior of quantum
correlations is different and more prominent as the noise rate decreases at the
considered period of time.