  A MEMS Duffing resonator is driven by two adjacent frequency tones into the
nonlinear regime. We show that if the two-tone drive is applied at a frequency
where a bistable response of the nonlinear oscillator exists, then the system
output will be modulated by a relaxation cycle caused by periodically jumping
between the two solution-branches of the bistable response. Although the jumps
are caused by the beating of the drives, the existence and period of this
relaxation or hysteresis cycle is not solely dictated by the beat frequency
between the two driving tones, but also by their amplitude and detuning with
respect to the device resonance frequency. We equally demonstrate how the
period of the cycles can be tuned via added tension in the device and how these
oscillations can be used as a means of sensitive pulse-width modulated (PWM)
readout of MEMS sensors.
