The Librator: A new dynamical regime for nonlinear microelectromechanical devices

Abstract

We present a novel mode of operation for Duffing-type nonlinear microelectromechanical (MEMS) devices whereby a self-sustained multi-frequency output is generated. This new librator regime creates a limit cycle around a dynamical fixed point, i.e. around fixed points within the rotating frame, whereas a traditional oscillator generates a limit cycle around a static fixed point. The librator limit cycles thus created do not change the global topology of the rotating frame phase space, but are constrained by it. Due to the Duffing nonlinearity different types of limit cycles could be generated within the same phase space, with each type possessing distinct dynamical features. Transitioning between these limit cycles requires crossing homoclinic bifurcations, which is done without generating chaos as the phase space dynamics are two dimensional. This work opens the possibility to the creation of a librator network in analogy with oscillator network, however this can be done in a single MEMS device.