Synchronization properties of self-sustained mechanical oscillators

We study, both analytically and numerically, the dynamics of mechanical oscillators kept in motion by a feedback force, which is generated electronically from a signal produced by the oscillators themselves. This kind of self-sustained systems may become standard in the design of frequency-control devices at microscopic scales. Our analysis is thus focused on their synchronization properties under the action of external forces and on the joint dynamics of two to many coupled oscillators. Existence and stability of synchronized motion are assessed in terms of the mechanical properties of individual oscillators, namely, their natural frequencies and damping coefficients, and synchronization frequencies are determined. Similarities and differences with synchronization phenomena in other coupled oscillating systems are emphasized.