梯形取样鉴相频率合成器的Hopf分岔集

Bifurcation and Chaos of the Ladder-shaped Sampling and Phase-detecting Frequency Synthesizer

分析和研究梯形取样鉴相频率合成器环的分岔现象 ,根据 Ushio与 Hira等人的方法 ,从理论上证明了当系统参数满足一定条件时 ,系统会出现分岔现象 ,具体计算出系统在各个不动点处的 Hopf分岔集 ,给出了分岔与系统参数的关系式 ,揭示了分岔与系统参数的内在联系 ;最后通过计算系统的李雅普诺夫指数以及豪斯道夫维数 ,进一步验证了梯形取样鉴相频率合成器环中混沌现象的存在性。

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.