  The generation of GHZ states calls for simultaneous excitation of multiple
qubits. The peculiarity of such states is reflected in their nonzero
distributed entanglement which is not contained in other entangled states. We
study the optimal way to excite three superconducting qubits through a common
cavity resonator in a circuit such that the generation of distributed
entanglement among them could be obtained at the highest degree in a
time-controllable way. A non-negative measure quantifying this entanglement is
derived as a time function of the quadripartite system evolution. We find that
this measure does not stay static but obtains the same maximum periodically.
When the qubit-resonator couplings are allowed to vary, its peak value is
enhanced monotonically by increasing the greatest coupling strength to one of
the qubits. The period of its peak to peak revival maximizes when the couplings
become inhomogeneous, thus qubit excitation becoming asynchronous, at a
relative ratio of 0.35. The study demonstrates the role of asynchronous
excitations for time-controlling multi-qubit systems, in particular in
extending entanglement time.
