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We present simulations of two-dimensional Josephson-junction arrays to study giant Shapiro steps in these arrays. The amplitude and frequency dependence of the step widths is found to be more complex than in single junctions. The fractional step widths are found to decrease more rapidly with increasing frequency or rf current than conventional steps in single junctions. The washboard model of single junctions is extended to arrays to explain these differences between arrays and single junctions.

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We present simulations of one- and two-dimensional Josephson-junction arrays to study the effects of disorder on the coherent oscillation of such arrays. For uniformity in the critical currents comparable to that which can be achieved with present technology, two-dimensional arrays are much more stable against disorder than one-dimensional arrays. Both systems are particularly sensitive to disorder when biased near the critical current, with stability increasing at currents farther above the critical current.