  The passive conserved Swift-Hohenberg equation (or phase-field-crystal [PFC]
model) corresponds to a gradient dynamics for a single order parameter field
related to density. It provides a simple microscopic description of the
thermodynamic transition between liquid and crystalline states. In addition to
spatially extended periodic structures, the model describes a large variety of
steady spatially localized structures. In appropriate bifurcation diagrams the
corresponding solution branches exhibit characteristic slanted homoclinic
snaking. In an active PFC model, encoding for instance the active motion of
self-propelled colloidal particles, the gradient dynamics structure is broken
by a coupling between density and an additional polarization field. Then,
resting and traveling localized states are found with transitions characterized
by parity-breaking drift bifurcations. Here, we first briefly review the
snaking behavior of localized states in passive and active PFC models before
discussing the bifurcation behavior of localized states in systems of (i) two
coupled passive PFC equations described by common gradient dynamics, (ii) two
coupled passive PFC where the coupling breaks the gradient dynamics structure,
and (iii) a passive PFC coupled to an active PFC.
