基于特定混沌系统微弱谐波信号频率检测的理论分析与仿真

Simulation and theoretical analysis on detection of the frequency of weak harmonic signals based on a special chaotic system

为更完整地研究一类特定的Duffing Holmes方程所建立的混沌系统用于确定微弱谐波未知频率 ,论证了方程存在周期解并且该解唯一 ;利用稳定相态周期轨迹特征成功地进行了确定谐波频率的仿真实验 ;从 1Hz至 2 0 0Hz变阻尼比 (α)计算了检测误差 |Δω|;结果表明 ,不同频率带宽、不同频率相应的α值选择需要经过细致仿真实验去加以确定 .

In order to study a kind of chaotic system which is based on the special Duffing-Homes equation, and use it to detect the unknown frequency of weak harmonious signals, we prove the existence of the periodic solution and the exclusivism of the solution, carry out simulation experiments to detect harmonious frequency using the periodic trajectory of a stable phase state.We also compute the detection error | &UDelta;ω| When the damping ratio (α) changes and the frequency changes from 1Hz to 200Hz. The results show that we have to choose the value of a corresponding to the different range of frequency by simulation experiments.