  We studied the geometric quantum discord of a quantum system consisted of a
Jaynes- Cummings atom, a cavity and an isolated atom. The analytical
expressions of the geometric quantum discord for two atoms, every atom with
cavity and the total system were obtained. We showed that the geometric quantum
discord is not always zero when entanglement fall in death for two-atom
subsystem; the geometric measurement of quantum discord of the total system
developed periodically with a single frequency if the initial state of two
atoms was not entangled, otherwise, it oscillates with two or four frequencies
according to the cavity is initially empty or not, respectively.
