A parametric oscillator is a harmonic oscillator whose parameters oscillate in time. In an important special case, a harmonically excited system turns into a parametrically excited oscillator when the amplitude of its actuating force is set to be a function of its states. Resonance for such a system completely differs from the harmonic excitation case in that it exhibits instability phenomena.

In this study the implementation of parametric resonance for improving the performance of MEMS gyroscopes is examined. The equation of motion for this gyroscope is a nonlinear Mathieu equation coupled to a Duffing equation. After presenting a parameter selection method, the stability of the system is examined by means of Floquet theory and the instability of the origin is shown to be related to the occurrence of parametric resonance. A bifurcation study is also performed in order to predict the existence of chaotic behavior.

This study indicates that a gyroscope undergoing parametric resonance can produce high output amplitudes as large as 5% of the drive amplitude; this is around 1000 times greater than that previously reported for gyroscopes but it still remains to put these results into practice.