  We discuss dynamics of a model of an energy transfer between dark energy (DE)
and dark matter (DM). The energy transfer is determined by a non-conservation
law resulting from a diffusion of dark matter in an environment of dark energy.
The relativistic invariance defines the diffusion in a unique way. The system
can contain baryonic matter and radiation which do not interact with the dark
sector. We treat the Friedman equation and the conservation laws as a closed
dynamical system. The dynamics of the model is examined using the dynamical
systems methods for demonstration how solutions depend on initial conditions.
We also fit the model parameters using astronomical observation: SNIa, $H(z)$,
BAO and Alcock-Paczynski test. We show that the model with diffuse DM-DE is
consistent with the data.
