  We study the problem of pattern selection in an array of
parametrically-driven nonlinear resonators with application to
microelectromechanical and nanoelectromechanical systems (MEMS & NEMS), using
an amplitude equation recently derived by Bromberg, Cross, and Lifshitz [PRE
73, 016214 (2006)]. We describe the transitions between standing-wave patterns
of different wave numbers as the drive amplitude is varied either
quasistatically, abruptly, or as a linear ramp in time. We find novel
hysteretic effects, which are confirmed by numerical integration of the
original equations of motion of the interacting nonlinear resonators.
