  This work investigates the behavior of an AlGaAs/GaAs piezoelectric nonlinear
MEMS oscillator exhibiting a 1:3 internal resonance. The device is explored in
an open-loop configuration, i.e. as a driven resonator, where depending on the
drive conditions we observe energy transfer between the first and third modes,
and the emergence of supercritical Hopf limit cycles. We examine the dependence
of these bifurcations on the oscillator's frequency and amplitude, and
reproduce the observed behavior using a system of nonlinearly coupled equations
which show interesting scaling behavior.
