When a discrete nonlinear array is driven across a periodic surface spatially coherent modes of motion can coexist associated with different average velocities due to resonant parametric forcing of the particle fluctuations by the center of mass motion. Depending on the coupling strength κ and size of the array N, jumps in the minimum friction (maximum velocity) exhibited by the array occur at κₘ(N)~(N/m)² as new modes stabilize and are selected by the dynamics. The existence of such coherent modes allows both an effective low dimensional description of the dynamics to exist and the possibility for control of friction close to these instabilities.
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Hentschel et al. (1999) studied this question.
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