Period doubling bifurcation in discrete phase-locked loops
Bifurcation theory is very important in digital phase-locked loops (DPLLs) which are frequently encountered in radio engineering and communication and have been used during 60 years. Calculation of bifurcation values of the parameters are very important problem for analysis of working regimes of DPLLs.
Mathematical model of discrete digital phase-locked loop with sinusoidal characteristic of phase discriminator is considered. The Feigenbaum effect for nonunimodal maps which describe such DPLL is investigated by theoretical approach and numerical calculations. Bifurcations parameters of period doubling bifurcation are calculated.