  The response of a coupled array of nonlinear oscillators to parametric
excitation is calculated in the weak nonlinear limit using secular perturbation
theory. Exact results for small arrays of oscillators are used to guide the
analysis of the numerical integration of the model equations of motion for
large arrays. The results provide a qualitative explanation for a recent
experiment [Buks and Roukes, cond-mat/0008211, to appear in J. MEMS (2002)]
involving a parametrically-excited micromechanical resonator array. Future
experiments are suggested that could provide quantitative tests of the
theoretical predictions.
