  We study the response of a large array of coupled nonlinear oscillators to
parametric excitation, motivated by the growing interest in the nonlinear
dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and
NEMS). Using a multiscale analysis, we derive an amplitude equation that
captures the slow dynamics of the coupled oscillators just above the onset of
parametric oscillations. The amplitude equation that we derive here from first
principles exhibits a wavenumber dependent bifurcation similar in character to
the behavior known to exist in fluids undergoing the Faraday wave instability.
We confirm this behavior numerically and make suggestions for testing it
experimentally with MEMS and NEMS resonators.
