混沌背景下信号的盲分离

混沌信号与确定性小信号叠加生成的混合信号是一更高维的混沌信号,因而不能用一般的混沌信号噪声抑制的方法进行分离.提出了一种这类信号盲分离的方法.在重构未知的混沌信号的动力方程时,充分利用混沌吸引子的几何特性,并且限定动力映射为原混沌吸引子所在流形的内部映射,从而保证了重构的动力系统方程对应于原混沌信号,而不是同样具有混沌特性的混合信号.然后利用重构的动力方程,借用混沌信号中的噪声抑制思想,估计出原混沌信号对应的轨道,实现信号分离.通过对Lorenz系统中谐波信号、Henon映象中自回归过程,以及脑电信号中谐波信号进行提取的数值实验,验证了信号盲分离方法的有效性和可行性. 关键词： 混沌 非线性 信号处理 盲分离     

混沌干扰中基于同步挤压小波变换的谐波信号提取方法

针对混沌干扰背景下多个谐波信号的提取问题, 提出了一种基于同步挤压小波变换(SST)的谐波信号抽取方法. 首先利用SST将混沌信号和谐波信号组成的混合信号分解为不同的内蕴模态类函数, 然后利用Hilbert变换对分离出的内蕴模态类函数进行频率识别, 从中分离出各谐波信号. 以Duffing混沌背景为例, 对混沌干扰下多谐波信号的提取进行了实验分析. 实验结果表明: 对于不同频率间隔的多个谐波分量, 本文方法的提取结果都具有较高的精度, 而且所提方法对高斯白噪声的干扰具有较好的鲁棒性, 综合提取效果优于经典的经验模态分解方法.     

基于小波变换的混沌信号相空间重构研究

应用小波变换和非线性动力学方法研究了混沌信号在相空间中的行为，指出混沌时间序 列的小波变换实质上是在重构的相空间中，混沌吸引子向小波滤波器向量所张的空间中的投 影，与Packard等人提出的相空间重构方法本质上是一致的.实验结果表明，混沌信号经过 小波变换后，吸引子轨迹与原有轨迹具有相似的结构，同时，系统的关联维数、Kolmogorov 熵等非线性不变量仍然得到保留.这些结果表明，利用小波变换研究混沌信号是有效的. 关键词： 小波变换 相空间重构 混沌信号 脑电信号     

基于经验模式分解的混沌干扰下谐波信号的提取方法

由混沌信号和谐波信号组合而成的复杂信号的分离方法一直受到关注.利用经验模式分解方法,依据任何信号由不同的固有简单振动模态组成的概念,将由混沌信号和谐波信号组合而成的复杂信号分离为不同的内在模态函数,并从中分解出谐波信号.通过利用Duffing方程产生的混沌信号进行的仿真实验,结果都表明该方法在一定参数范围内非常有效. 关键词： 经验模式分解 混沌 信号处理     

半周期延迟-非线性反馈控制混沌

提出了基于稳定性准则的半周期延迟-非线性反馈控制混沌的方法，即SC(stability criterion)半周期延迟非线性反馈控制法.通过对混沌系统的适当分离，得到一个特殊的非线性函数，并利用混沌输出信号与其半周期延迟信号的非线性函数之和，构造了连续反馈输入干扰.该方法继承了延迟反馈控制方法及稳定性准则控制方法的优点，实现了有效的自控制过程；并克服了延迟反馈方法的限制，能将嵌入混沌吸引子中的自对称直接不稳周期轨稳定.控制过程可随时开始，具有简便、灵活性.数值模拟结果显示了SC半周期延迟-非线性反馈方法控制的有效性. 关键词： 稳定性准则 混沌控制 半周期延迟 非线性反馈     

一种恒Lyapunov指数谱混沌吸引子及其Jerk电路实现

基于Colpitts方程,提出了一种新的三维混沌吸引子.该混沌吸引子在系统变幅参数改变时,输出混沌信号中的两维信号的幅值随着参数作线性变化,第三维信号的幅值保持在同样的数值区间,而系统的Lyapunov指数谱却保持恒定.该混沌系统通过改造Colpitts混沌系统归一化方程中的指数项为绝对值项而得到.通过相图、庞加莱映射、功率谱以及Lyapunov指数,证明了该混沌吸引子的存在性.对这种新型混沌吸引子的基本动力学行为予以分析,基于Lyapunov指数谱阐述并论证了该系统能够呈现周期态和混沌态.最后,给出该特 关键词： Colpitts系统 恒定Lyapunov指数谱 混沌吸引子 分岔图     

含三个忆阻器的六阶混沌电路研究

利用两个磁控忆阻器和一个荷控忆阻器设计了一个六阶混沌电路,并建立了相应电路状态变量的非线性动力学方程.研究了系统的基本动力学特性,平衡点及其稳定性分析表明:该电路具有一个位于忆阻器内部状态变量所构成三维平衡点集,平衡点的稳定性由电路参数和三个忆阻器的初始状态决定.分岔图、Lyapunov指数谱等表明该电路在参数变化情况下能产生Hopf分岔和反倍周期分岔两种分岔行为,以及超混沌、暂态混沌、阵发周期现象等多种复杂的非线性动力学行为.将观察混沌吸引子时关注的电压、电流信号推广到功率和能量信号,观察到了莲花型、叠加型吸引子等奇怪吸引子的产生.并研究了各忆阻器能量信号之间产生吸引子的情况,特别地,当取不同的初始值时,系统出现了共存混沌吸引子和周期极限环与混沌吸引子的共存现象.     

混沌背景中信号参数估计的新方法

怎样提取混沌背景中信号的参数具有重要意义.在重构的相空间中,叠加有其他信号的混沌信号时间序列重构的点集会偏离混沌吸引子所在光滑流形,依据这一性质并综合利用混沌背景中信号本身的特性,提出一种参数估计的新方法：最小相对奇异值(MRSV)法.该方法先建立逆滤波器,由其输出重构相空间,然后改变其参数,使输出信号在嵌入空间中作局部奇异值分解的相对奇异值最小,来实现参数估计.AR模型参数和正弦信号频率估计的仿真结果验证了该方法的有效性. 关键词： 混沌 参数估计 最小相对奇异值(MRSV) 逆滤波器     

一个四翼混沌吸引子

在新的四维混沌系统中数值观察到四翼混沌吸引子，然而，通过进一步分析发现，该四翼吸引子并非真实的，实际上它是上、下两个共存的双翼混沌吸引子，他们各自有独立的混沌吸引域，由于其位置靠得太近和数值误差产生的一种假象.通过引入一个线性状态反馈控制项，系统的一些相似性被破坏，受控系统能产生穿越上下吸引域界限的对角双翼混沌吸引子，进一步，随着动力学模态的演化，上下混沌吸引子与对角混沌吸引子融合成一个真正的四翼混沌吸引子.最后，通过比较该四翼混沌吸引子的系统、Lorenz系统、Chua氏电路等混沌信号的频谱发现，四翼混沌吸引子的系统信号具有极宽的频谱带宽，该特性在通讯加密等工程应用中具有重要价值. 关键词： 四维混沌系统 双翼吸引子 四翼吸引子 频谱分析     

均匀湍流中的奇怪吸引子

本文对于实测的湍流信号采用延迟坐标重建相空间技术计算了它的关联维数,熵和最大Лялнов指数,从而指出这是一种受随机噪声干扰的确定性的混沌现象,它在相空间的吸引子是一个随机噪声背景上的奇怪吸引子。     

Chaotic signal detection and estimation based on attractor sets: applications to secure communications

We consider the problem of detection and estimation of chaotic signals in the presence of white Gaussian noise. Traditionally this has been a difficult problem since generalized likelihood ratio tests are difficult to implement due to the chaotic nature of the signals of interest. Based on Poincare's recurrence theorem we derive an algorithm for approximating a chaotic time series with unknown initial conditions. The algorithm approximates signals using elements carefully chosen from a dictionary constructed based on the chaotic signal's attractor. We derive a detection approach based on the signal estimation algorithm and show, with simulated data, that the new approach can outperform other methods for chaotic signal detection. Finally, we describe how the attractor based detection scheme can be used in a secure binary digital communications protocol.     

Denoising of chaotic signal using independent component analysis and empirical mode decomposition with circulate translating

In this paper, a new method to reduce noises within chaotic signals based on ICA(independent component analysis)and EMD(empirical mode decomposition) is proposed. The basic idea is decomposing chaotic signals and constructing multidimensional input vectors, firstly, on the base of EMD and its translation invariance. Secondly, it makes the independent component analysis on the input vectors, which means that a self adapting denoising is carried out for the intrinsic mode functions(IMFs) of chaotic signals. Finally, all IMFs compose the new denoised chaotic signal. Experiments on the Lorenz chaotic signal composed of different Gaussian noises and the monthly observed chaotic sequence on sunspots were put into practice. The results proved that the method proposed in this paper is effective in denoising of chaotic signals.Moreover, it can correct the center point in the phase space effectively, which makes it approach the real track of the chaotic attractor.     

Boundary crisis and transient in a dissipative relativistic standard map

Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent −1 is observed.     

The open-plus-closed loop （OPCL） method for chaotic systems with multiple strange attractors

Based on the open-plus-closed-loop (OPCL) control method a systematic and comprehensive controller is presented in this paper for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). Results show that the final structure of the suggested controller for stabilization has a simple linear feedback form. To keep the integrity of the suggested approach, the globality proof of the basins of entrainment is also provided. In virtue of the OPCL technique, three different kinds of chaotic controls of the system are investigated, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one; and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the proposed means.     

Monitoring changes in time of chaotic nonlinear systems

We extend our method for classifying signals from chaotic nonlinear dynamical systems to the problem of monitoring chaotic nonlinear dynamical systems with the goal of detecting that the state of a system has changed. One potential application would be to systems where the changes are not easily detectable by spectral analysis or other linear techniques. The method is expected to be most useful in comparison to other techniques when there are other signals or noise present, some of which have a broad band frequency spectrum, and the signal of interest is associated with either a low dimensional dynamical system or a low dimensional chaotic attractor. The method is applied to data from a laboratory model of a fluidized bed reactor and to data from a gyroscope as well as to numerically generated signals from mathematical models. For the dynamical systems considered in the paper, the proposed method provides significantly better discrimination than spectral analysis. (c) 1995 American Institute of Physics.     

Detecting variation in chaotic attractors

If the output of an experiment is a chaotic signal, it may be useful to detect small changes in the signal, but there are a limited number of ways to compare signals from chaotic systems, and most known methods are not robust in the presence of noise. One may calculate dimension or Lyapunov exponents from the signal, or construct a synchronizing model, but all of these are only useful in low noise situations. I introduce a method for detecting small variations in a chaotic attractor based on directly calculating the difference between vector fields in phase space. The differences are found by comparing close strands in phase space, rather than close neighbors. The use of strands makes the method more robust to noise and more sensitive to small attractor differences.     

TS fuzzy realization of chaotic Lü system

The Lü attractor is a new chaotic attractor, which connects the Lorenz attractor and the Chen attractor and represents the transition from one to the other. The Letter presents a hybrid TS fuzzy modeling approach for the newly coined chaotic Lü system. Then the abundant and fundamental dynamical behaviors of the chaotic Lü system are completely and comprehensive investigated based on this novel hybrid TS fuzzy model.     

基于混沌吸引子形态特性的两相流流型分类方法研究

利用高灵敏度差压传感器，在垂直上升管中采集到了80组气液两相流差压波动信号.利用放置参考截面的方法，建立了描述混沌吸引子形态的一般方法，在此基础上，提出了不同维数下的吸引子形态特征量进行组合的气液两相流流型分类新方法.研究结果表明：该方法对包括复杂过渡流型在内的气液两相流流型有很好分类效果，预示着混沌吸引子形态描述是研究非线性时间序列的实用有效途径. 关键词： 气液两相流 流型分类 吸引子形态 混合维     

Double Poincaré sections of a quasi-periodically forced,chaotic attractor

A nonlinear mechanical oscillator is forced with two incommensurate harmonic signals and chaotic vibrations are experimentally observed. The fractal nature of this strange attractor in four-dimensional phase space is revealed by using a double Poincaré section. This section involves a narrow timing pulse on one harmonic driving signal and a wider phase window on the other forcing harmonic signal. The resulting two-dimensional map shows a Cantor set structure characteristic of strange attractors. The transition from quasi-periodic to chaotic vibrations is also observed.