  We investigate the dynamics of global entanglement, the Meyer-Wallach
measure, under decoherence, analytically. We study two important class of
multi-partite entangled states, the Greenberger-Horne-Zeilinger and the W
state. We obtain exact results for various models of system-environment
interactions (decoherence). Our results shows distinctly different scaling
behavior for these initially entangled states indicating a relative robustness
of the W state, consistent with previous studies.
