  We investigate the decay of the global entanglement, due to decoherence, of
multiqubit systems interacting with a reservoir in a non Markovian regime. We
assume that during the decoherence process each qubit of the system interacts
with its own, independent environment. Most previous works on this problem
focused on particular initial states or families of initial states amenable of
analytical treatment. Here we determine numerically the typical, average
behaviour of the system corresponding to random initial pure states uniformly
distributed (in the whole Hilbert space of $n$-qubit pure states) according to
the Haar measure. We study systems consisting of 3, 4, 5, and 6 qubits. In each
case we consider also the entanglement dynamics corresponding to important
particular initial states, such as the GHZ states or multiqubit states
maximizing the global entanglement, and determine in which cases any of these
states is representative of the average behaviour associated with general
initial states.
