Effect of the green noise on the phase-locked-loop frequency-control system

The operation of the phase-locked-loop frequency-control system under the action of low-passfiltered broadband stationary noise (green noise) is considered. In order to analyze such systems, an averaging method that takes into account the external noise in a zeroth-order approximation has been constructed. Notions of an effective potential and correction process have been introduced and their role in the development of the dynamics of the system has been determined. A numerical experiment has been performed, which confirms the theoretical conclusions.