Abstract
In dissipationless linear lattices, spatial disorder or quasiperiodic modulations in on-site potentials induce localization of the eigenstates and block the spreading of wave packets. Quasiperiodic inhomogeneities allow for the metal–insulator transition at a finite modulation amplitude already in one dimension. We go beyond the dissipationless limit and consider nonlinear quasi-periodic arrays that are additionally subjected to dissipative losses and energy pumping. We find finite excitation thresholds for oscillatory phases in both metallic and insulating regimes. In contrast to disordered arrays, the transition in the metallic and weakly insulating regimes display features of the second order phase transition accompanied by a large-scale cluster synchronization. In the limit of strong localization, we find the existence of globally stable asymptotic states consisting of several localized modes. These localization attractors and chaotic synchronization effects can be potentially implemented with polariton condensate lattices and cavity-QED arrays.
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