  We study the time evolution of $N_q$ two-level atoms (or qubits) interacting
with a single mode of the quantised radiation field. In the case of two qubits,
we show that for a set of initial conditions the reduced density matrix of the
atomic system approaches that of a pure state at $\sfrac{t_r}{4}$, halfway
between that start of the collapse and the first mini revival peak, where $t_r$
is the time of the main revival. The pure state approached is the same for a
set of initial conditions and is thus termed an `attractor state'. The set
itself is termed the basin of attraction and the features are at the center of
our attention. Extending to more qubits, we find that attractors are a generic
feature of the multi qubit Jaynes Cummings model (JCM) and we therefore
generalise the discovery by Gea-Banacloche for the one qubit case. We give the
`basin of attraction' for $N_q$ qubits and discuss the implications of the
`attractor' state in terms of the dynamics of $N_q$-body entanglement. We
observe both collapse and revival and sudden birth/death of entanglement
depending on the initial conditions.
