Synchronization and chaos in a real discrete phase-locked loop

Attempts an experimental verification of a certain model of the discrete phase-locked loop (DPLL), whose behavior is typical for a wide class of DPLLs with a positive-going zero-crossing detector. The theoretical model is described by a one-dimensional dynamical system (an endomorphism of the circle S/sup 1/). The model proved to agree well with the experimental system. In a wide range of parameters (amplitude and frequency of the input signal), the DPLL works as a frequency divider. Out of the phase-locked region, the loop is not globally stable and a stable periodic oscillation with very long period appeared together with chaotic oscillations.<>