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Dynamical evolution of global quantum discord (GQD) and von Neumann entropy (VNE) is studied for N two-level atomic system (TLS) (two, three and four TLS). The system interacts with the single mode Fock field and the cavity is filled with the non-linear Kerr medium (NLKM). It is seen that for large values of the Kerr parameter, the GQD and VNE show periodic behavior which leads to the sudden death and birth of the quantum entanglement (QE). It is found that the oscillations of the GQD is suppressed for the initial mixed state. The VNE has non-zero values of quantum interference throughout the dynamics of the system for initial mixed states. It is also found that the multipartite systems show sustained response to the QE during the time evolution. Moreover, the GQD and VNE are notably affected in the presence of the NLKM and affected for the entire range of Kerr values as we increase the number of photons in the cavity. Furthermore, for both initial pure and mixed states, the periodic behavior of the GQD and VNE is almost the same for the case of moving TLS. The sudden death and birth of QE is more prominent for moving TLS case. The atomic motion is favorable to sustain the QE in the atomic systems in a NLKM.

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