  A lattice dynamics model is proposed for the history dependence observed in
sandpile experiments. The dependence of the stress distribution on the
preparation of the sandpile is explained as a dependence of certain attractors
on the preparation of the system. The model has three phases, but the history
dependence is shown to exist only in the phase where a perturbation is
amplified selectively rather than globally when propagating in the downflow
direction. The condition for this history dependence is given in terms of the
spatial Lyapunov exponent.
