Perturbation of a harmonic oscillator by small modulated signals

A generalized Adler equation is derived through the use of a theorem of Kudrewicz (1975). The equation describes the phase difference between the perturbed and perturbing signal as a function of time. The phenomenon corresponding to a time-limited phase difference is called q-locking, and the region in parameter space in which the phenomenon occurs is called the q-locking region. By the use of a proposition of Tykhonov, the size of the q-locking regions for the cases of small perturbing signals slowly modulated in amplitude and phase is determined, and the behavior of the phase difference outside the q-locking regions is described.