  Two-dimensional spatially localized structures in the complex Ginzburg-Landau
equation with 1:1 resonance are studied near the simultaneous occurrence of a
steady front between two spatially homogeneous equilibria and a supercritical
Turing bifurcation on one of them. The bifurcation structures of steady
circular fronts and localized target patterns are computed in the Turing-stable
and Turing-unstable regimes. In particular, localized target patterns grow
along the solution branch via ring insertion at the core in a process
reminiscent of defect-mediated snaking in one spatial dimension. Axisymmetric
oscillons on these solution branches are found to be stable over a wide
parameter interval, and subject to various types of instability otherwise.
Direct numerical simulations reveal novel depinning dynamics of localized
target patterns in the radial direction, and of circular and planar localized
hexagonal patterns in the fully two-dimensional system.
