Synchronization in a discrete phase-locked loop

A 1-D model of the discrete phase-locked loop (DPLL) is examined. When calculating synchronization zones in a circuit it is customary to use the rotation number as the basis. There are systems in which rotation-number bifurcation takes place, such as a VCO, whose rotation number is, for fixed values of the parameters, an interval, not a single point. It is proposed that the ends of the interval be obtained from the so-called upper and lower functions. The theoretical analysis has been confirmed by computation experiments