Bifurcation and Chaos of the Ladder-shaped Sampling and Phase-detecting Frequency Synthesizer
Tang Yong · 2001
The bifurcation phenomena of the ladder sampled phase demodulation frequency synthesizer is analyzed and studied. According to the method of Ushio and Hiral etc, It is theoretically proved that the system has a bifurcation output when certain requirements of the system parameters are satisfied. Hopf bifurcation set of every fixed point of the system is particularly calculated, and the relative formulas of bifurcation and the parameter of the system are given. The internal relations of bifurcation and the parameter of the system are revealed. Lyapunov numbers and Hausdorf dimension are calculated at last, and the phenomena of chaos the ladder sampled Phase Demodulation Frequency Synthesizer are further verified.