  We study a system of active particles with soft repulsive interactions that
lead to an active cluster-crystal phase in two dimensions. We use two different
modelizations of the active force - Active Brownian particles (ABP) and
Ornstein-Uhlenbeck particles (AOUP) - and focus on analogies and differences
between them. We study the different phases appearing in the system, in
particular, the formation of ordered patterns drifting in space without being
altered. We develop an effective description which captures some properties of
the stable clusters for both ABP and AOUP. As an additional point, we confine
such a system in a large channel, in order to study the interplay between the
cluster crystal phase and the well-known accumulation near the walls, a
phenomenology typical of active particles. For small activities, we find
clusters attached to the walls and deformed, while for large values of the
active force they collapse in stripes parallel to the walls.
