Limit cycles and bifurcations in a nonlinear MEMS oscillator with a 1:3 internal resonance. Part I: The case of a driven resonator

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.