  We examine the evolution of an inhomogeneous mixture of non-relativistic
pressureless cold dark matter (CDM), coupled to dark energy (DE) characterised
by the equation of state parameter $w<-1/3$, with the interaction term
proportional to the DE density. This coupled mixture is the source of a
spherically symmetric Lema\^\ itre-Tolman-Bondi (LTB) metric admitting an
asymptotic Friedman-Lema\^\ itre-Robertson-Walker (FLRW) background. Einstein's
equations reduce to a 5-dimensional autonomous dynamical system involving
quasi--local variables related to suitable averages of covariant scalars and
their fluctuations. The phase space evolution around the critical points
(past/future attractors and five saddles) is examined in detail. For all
parameter values and both directions of energy flow (CDM to DE and DE to CDM)
the phase space trajectories are compatible with a physically plausible early
cosmic times behaviour near the past attractor. This result compares favourably
with mixtures with the interaction driven by the CDM density in which
conditions for a physically plausible past evolution are more restrictive.
Numerical examples are provided describing the evolution of an initial profile
that can be associated with idealised structure formation scenarios
