  The exploration of the phase diagram of a minimal model for barchan fields
leads to the description of three distinct phases for the system: stationary,
percolable and unstable. In the stationary phase the system always reaches an
out of equilibrium, fluctuating, stationary state, independent of its initial
conditions. This state has a large and continuous range of dynamics, from
dilute -- where dunes do not interact -- to dense, where the system exhibits
both spatial structuring and collective behavior leading to the selection of a
particular size for the dunes. In the percolable phase, the system presents a
percolation threshold when the initial density increases. This percolation is
unusual, as it happens on a continuous space for moving, interacting, finite
lifetime dunes. For extreme parameters, the system exhibits a sub-critical
instability, where some of the dunes in the field grow without bound. We
discuss the nature of the asymptotic states and their relations to well-known
models of statistical physics.
