  Analytical solution and entanglement swapping of a double Jaynes-Cummings
model in non-Markovian environments are investigated by the timeconvolutionless
master equation method. We obtain the analytical solution of this model and
discuss in detail the influence of atom-cavity coupling, non-Markovian effect
and initial state purity on entanglement dynamics. The results show that, in
the non-Markovian environments, the entanglement between two cavities can be
swapped to other bipartite subsystems by interaction between an atom and its
own cavity. Due to the dissipation of environment, the entanglements of all
bipartite subsystems will eventually decay to zero when the atom couples weakly
to its cavity and the non-Markovian effect is also weak. All bipartite
subsystems can tend to steady entanglement states if and only if there is the
strong atom-cavity coupling or the strong non-Markovian effect. The steady
state of the subsystem composed of an atom and its own cavity is independent on
the purity but the steady states of other bipartite subsystems are dependent on
the purity.
