用一类特定的双耦合Duffing振子系统检测强色噪声背景中的周期信号

通过分析耦合参数作用、系统所呈现大尺度周期相态的复杂性以及与系统在无噪声条件下状态的比较，得出耦合振子系统的动力学行为比同类单振子系统的复杂，周期相态更稳定、抗噪能力更强.用构造的一类含特定恢复力项双中强度耦合Duffing振子系统检测色噪声背景中的谐波、方波信号，信噪比分别达到-111.0和-108.45dB. 关键词： 特定双耦合 Duffing振子系统 色噪声 周期信号 信噪比     

混沌振子系统周期解几何特征量分析与微弱周期信号的定量检测

提出了一种对微弱周期信号的定量检测方法.分析混沌振子系统在大尺度周期状态下的相对稳定输出时,发现了混沌振子系统输出周期解的平均面积是一个比较稳定的几何特征量.该几何特征量与待测信号幅值之间存在比较稳定的单调递增关系.在一定的参数条件下,几何特征量精度可达到10^-6V².利用混沌系统对随机噪声信号的免疫性和对微弱周期信号的敏感性,进一步建立了微弱周期信号的定量检测方法.仿真实验表明,随着待检测幅度的增加,在保证检测精度的同时,抗噪性能也随之增强. 关键词： 混沌振子系统 大尺度周期相态 周期解的几何特征量 微弱周期信号的定量检测     

The bifurcation threshold value of the chaos detection system for a weak signal＊

Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detectionsystem for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detectionare correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system fora weak signal is established by using the theory of linear differential equation with periodic coefficients and computingthe Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system isdefined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of thechaos detection svstem.     

Physical mechanism of the chaotic detection of the unknown frequency of weak harmonic signal and effects of damping ratio on the detection results

In the zero-order approximation, we use the perturbation method of parameter with small magnitude to prove that the harmonic frequency in the solution of the equation is close to that of the driving force when the chaotic system from Duffing－Holmes equation stays in the stable periodic state, which is the physical mechanism of the detection of the unknown frequency of weak harmonic signal using the chaotic theory. The result of the simulation experiment shows that the method proposed in this paper, by which one can determine the frequency of the stable system from the number of circulation change of the phase state directionally across a fixed phase state point (x,\dot{x}) in fixed simulation time period, is successful. Analyzing the effects of the damping ratio on the chaotic detection result, one can see that for different frequency ranges it is necessary to carefully choose corresponding damping ratio α.     

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

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200Hz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. 关键词： 特定混沌系统 混沌系统周期解 稳定相态周期 阻尼比     

Analysis of a kind of Duffing oscillator system used to detect weak signals

The stability of the periodic solution of the Duffing oscillator system in the periodic phase state is proved by using the Yoshizaw theorem, which establishes a theoretical basis for using this kind of chaotic oscillator system to detect weak signals. The restoring force term of the system affects the weak-signal detection ability of the system directly, the quantitative relationship between the coefficients of the linear and nonlinear items of the restoring force of the Duffing oscillator system and the SNR in the detection of weak signals is obtained through a large number of simulation experiments, then a new restoring force function with better detection results is established.     

色噪声背景下微弱正弦信号的混沌检测

提出一种利用混沌在特定状态下对参数的敏感性来实现微弱正弦信号检测的新方案-该方案可以有效地将深陷在色噪声背景中的微弱正弦信号检测出来-给出了混沌检测的方法,分析了混沌检测中噪声对系统状态的影响-仿真实验表明该混沌检测系统对小信号非常敏感，对任何零均值色噪声均具有极强的抑制能力- 关键词： 微弱正弦信号 混沌检测 色噪声 信噪比     

Regular nonlinear response of the driven Duffing oscillator to chaotic time series

Nonlinear response of the driven Duffng oscillator to periodic or quasi-periodic signals has been well studied.In this paper,we investigate the nonlinear response of the driven Duffng oscillator to non-periodic,more specifically,chaotic time series.Through numerical simulations,we find that the driven Duffng oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model,and there exists a relationship between the state of the driven Duffng oscillator and the chaoticity of the input signal of the driven Duffng oscillator.One real-world and two artificial chaotic time series are used to verify the new feature of Duffng oscillator.A potential application of the new feature of Duffng oscillator is also indicated.