  A detailed treatment of the entanglement dynamics of two distant but
non-identical systems is presented. We study the entanglement evolution of two
remote atoms interacting independently with a cavity field, as in the double
Jaynes-Cummings (JC) model. The four-qubit pairwise concurrences are studied,
allowing for asymmetric atom-cavity couplings and off-resonant ineractions.
Counter to intuition, imperfect matching can prove advantageous to entanglement
creation and evolution. For two types of initial entanglement, corresponding to
spin correlated and anti-correlated Bell states \Phi and \Psi, a full, periodic
and directed transfer of entanglement into a specific qubit pair is possible,
for resonant interactions, depending on the choice of relative couplings.
Furthermore, entanglement transfer and sudden death (ESD) can be prevented
using off-resonant interactions, although for some initial states, detunings
will trigger an otherwise frozen entanglement, to allow a full entanglement
transfer. We confirm a conservation rule governing the pairwise entanglement
between the non-interacting systems, that for the initial state \Psi the sum of
the square of these concurrences (SSC) is conserved. For \Phi, the total SSC is
reduced periodically, even to zero in some cases, to reveal a complete and
abrupt loss of all non-local pairwise entanglement.
