Synchronization characteristics of an array of coupled MEMS limit cycle oscillators

Abstract

The dynamics of a proposed microelectromechanical system (MEMS) consisting of an array of limit cycle oscillators (LCOs) are analyzed. The LCOs have dissimilar limit cycle frequencies and are coupled in a nearest-neighbor configuration via electrostatic fringing fields. The emergence of synchrony in the array is outlined for two cases: self-synchronization of the array to a single frequency, and entrainment of the array to an external inertial drive. Numerical analysis is used to study the dependence of synchrony on system parameters such as the coupling strength, detuning in the array, inertial drive strength, and frequency of the inertial drive. It is shown that the route to synchrony is complex due to the formation of frequency clusters. The limit cycle frequency of a single equivalent oscillator, with parameters averaged over the array is used as an estimate for the frequency of locking for the array. This equivalent oscillator is used to approximate the entire array and perturbation methods are applied to it. The perturbation method qualitatively captures the entrainment characteristics of the externally-driven array. This analysis is also used to track the complex sequence of bifurcations that occur as the drive strength changes, and to estimate the threshold drive strength for entrainment.