Spatially extended dynamical systems subjected to a periodic external input are able to store short-term memories as a result of self-organization. This phenomenon has been used to interpret sliding charge density wave experiments, and has
been found in lattices of coupled maps and oscillators. In this paper, we aim to describe the influence of a stochastic perturbation in the self-organized memories in a lattice of coupled linear and weakly nonlinear maps. We consider the case
in which the coupling between maps depends on the lattice distance as a power law.
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