  In dissipationless linear media, spatial disorder induces Anderson
localization of matter, light, and sound waves. The addition of nonlinearity
causes interaction between the eigenmodes, which results in a slow wave
diffusion. We go beyond the dissipationless limit of Anderson arrays and
consider nonlinear disordered systems that are subjected to the dissipative
losses and energy pumping. We show that the Anderson modes of the disordered
Ginsburg-Landau lattice possess specific excitation thresholds with respect to
the pumping strength. When pumping is increased above the threshold for the
band-edge modes, the lattice dynamics yields an attractor in the form of a
stable multi-peak pattern. The Anderson attractor is the result of a joint
action by the pumping-induced mode excitation, nonlinearity-induced mode
interactions, and dissipative stabilization. The regimes of Anderson attractors
can be potentially realized with polariton condensates lattices, active
waveguide or cavity-QED arrays.
