基于相空间邻域的混沌时间序列自适应预测滤波器(Ⅱ)非线性自适应滤波

根据相空间重构理论、最小均方误差准则和最陡下降原理，提出了一种基于相空间邻域的非线性自适应滤波算法.实验结果表明：这种非线性自适应预测滤波器能够有效预测一些混沌序列，在某种程度上具有抗噪声的能力. 关键词： 混沌时间序列 重构矢量 最小均方误差准则 非线性自适应预测     

基于差分进化算法的混沌时间序列预测模型参数组合优化

为了提高混沌时间序列预测模型的预测精度,提出一种基于差分进化（DE）算法的相空间重构和最小二乘支持向量机（LSSVM）模型参数组合优化方法．该方法将相空间重构参数和LSSVM预测模型参数进行组合作为差分进化算法的个体,以混沌时间序列预测精度作为个体的适应度函数,通过循环迭代获得最优参数组合．几个混沌时间序列的仿真实验结果表明,与传统的优化方法相比,参数组合优化方法具有更高的预测精度．     

道路交通流状态的多参数融合预测方法

针对道路交通流普遍存在的混沌特性以及单交通参数不足 以全面反映交通流状态的实际情况,考虑交通动力学系统中多个 交通参数之间的关联关系,提出一种新的多参数混沌时间序列预 测算法.该算法在相空间重构理论的基础上,借助Bayes估计将多个参数在 同一高维相空间中进行相点最优融合,从而增加重构相空间的系统信息量, 使得相空间的相点轨迹更加逼近原交通系统的动力学行为.同时借鉴单 参数混沌时间序列预测方法,从不同角度对动力学系统的运动状态进行描 述,以实现多参数时间序列的混沌预测.实验结果表明,通过融合多交通参数时 间序列,获得了更加完整的交通流状态变化特征.与单交通参数时间序列的预测 结果相比,其预测误差显著降低,均衡系数相应增大,提高了交通流状态预测的准确率.     

多元混沌时间序列的多核极端学习机建模预测

多元混沌时间序列广泛存在于自然、经济、社会、工业等领域. 对多元混沌时间序列进行建模预测有助于人类更好地管理, 控制与决策. 针对多元混沌时间序列的建模预测问题, 本文提出一种基于多核极端学习机的预测方法. 首先对多元混沌时间序列进行相空间重构, 将多元混沌时间序列序列的时间相关性转化为空间相关性. 提出一种结合多核学习算法与核极端学习机模型的多核极端学习机建立相空间中输入输出数据的非线性映射. 多核极端学习机模型结合了多核学习算法的数据融合能力以及核极端学习机的训练简便优势. 基于Lorenz混沌时间序列预测和San Francisco河流月径流量预测的仿真实验表明, 与其他常见混沌时间序列预测方法相比, 本文提出的基于多核极端学习机的多元混沌时间序列预测方法具有更小的预测误差.     

基于条件熵扩维的多变量混沌时间序列相空间重构

提出一种多变量混沌时间序列相空间重构的条件熵扩维方法.首先使用互信息法求解每个变量的时间延迟,其次按条件熵最大原则逐步扩展相空间的嵌入维数,使得重构坐标从低维到高维的转换保持较强的独立性,最终的重构相空间具有较低的冗余度,为多变量时间序列的预测构造了有效的模型输入向量.通过对几个经典多变量混沌时间序列进行数值实验,结果表明该方法比单变量预测和已有多变量预测方法具有更好的预测效果,说明了该重构方法的有效性. 关键词： 多变量混沌时间序列 相空间重构 条件熵 神经网络预测     

混沌时间序列的Volterra自适应预测

基于混沌动力系统相空间的延迟坐标重构,提出了一种预测混沌时间序列的Volterra自适应滤波预测法,对8种低维混沌序列采用二阶Volterra自适应滤波器进行预测的实验结果表明:当滤波器的长度Nl足够大时,Volterra自适应滤波器能够有效地预测低维混沌时间序列,且Nl的选择不仅与D2有关,还与混沌映射的光滑程度有关 关键词：     

基于混合神经网络和注意力机制的混沌时间序列预测

为提高混沌时间序列的预测精度,提出一种基于混合神经网络和注意力机制的预测模型(Att-CNNLSTM),首先对混沌时间序列进行相空间重构和数据归一化,然后利用卷积神经网络(CNN)对时间序列的重构相空间进行空间特征提取,再将CNN提取的特征和原时间序列组合,用长短期记忆网络(LSTM)根据空间特征提取时间特征,最后通过注意力机制捕获时间序列的关键时空特征,给出最终预测结果.将该模型对Logistic,Lorenz和太阳黑子混沌时间序列进行预测实验,并与未引入注意力机制的CNN-LSTM模型、单一的CNN和LSTM网络模型、以及传统的机器学习算法最小二乘支持向量机(LSSVM)的预测性能进行比较.实验结果显示本文提出的预测模型预测误差低于其他模型,预测精度更高.     

基于相空间邻域的混沌时间序列自适应预测滤波器(Ⅰ)线性自适应滤波

提出了一种基于相空间邻域的线性自适应滤波算法，将时间域变换到高维重构矢量空间，使 得不可能实现的线性预测变成了可能.实验结果表明：这种基于相空间邻域的线性自适应预 测滤波器能够有效预测一些混沌序列，能够检测到一些混沌载波中的信号，具有去混沌噪声 的能力. 关键词： 混沌时间序列 重构矢量 自适应预测     

基于径向基神经网络预测的混沌时间序列嵌入维数估计方法

根据Takens定理,研究了混沌时间序列相空间重构嵌入维数的选取问题.提出了基于径向基函数神经网络预测模型性能的嵌入维数估计方法,即根据嵌入维数与混沌时间序列预测模型性能的变化关系来确定嵌入维数.通过对几种典型混沌动力学系统的数值验证,结果表明该方法能够确定出合适的相空间重构嵌入维数. 关键词： 混沌 相空间重构 嵌入维数 预测     

Dicke模型的量子混沌和单粒子相干动力学特性

量子化的Dicke模型在非旋波近似条件下表现为量子混沌动力学特征.利用单粒子一阶时间关联函数,通过数值计算详细考察了Dicke模型中单粒子相干动力学特性.结果表明:当初始相干态处在混沌区域时,一阶时间关联函数曲线衰减较快,而当初始相干态处在规则区域时,一阶时间关联函数曲线衰减较慢,单粒子相干动力学对初态具有较强的敏感性,经典混沌抑制量子相干.考察单粒子相干动力学在相空间的平均演化性质,得到一种较好的量子经典对应关系.最后研究了相空间单粒子相干的整体动力学性质,更好地揭示了相空间的混沌和规则结构.     

基于递归量化分析与支持向量机的癫痫脑电自动检测方法

癫痫脑电信号的自动检测对癫痫的临床诊断与治疗具有重要意义.基于递归图(recurrence plot)的递归量化分析(recurrence quantification analysis,RQA)重现了非线性时间序列的动力学行为,分析了其递归特性,本文提出了基于RQA的癫痫脑电信号特征提取方法.实验结果表明:直接基于RQA特征的癫痫脑电的检测准确率较高,其中直接基于确定率DET的分类准确率可达到90.25%.本文还把提取的RQA特征值和变化系数、波动指数相结合组成特征向量,输入到SVM分类器,实现癫痫脑电信号的自动检测;实验结果表明:该方法的分类准确率可达到99%.     

用RQA 法分析不同信噪比下的非线性系统

以Lorenz系统为例，运用重现图形和重现定量分析法分析了不同信噪比下噪声对连续系统混沌区非线性特征量的影响．选取自相关函数第一次降到C(0)／2时所对应的t作为延迟时间τ，运用错误近邻分析法确定序列的嵌入维m，以重构相空间．结果表明：当信噪比大于5时，序列存在的确定性规律RPA仍能显示出来．随着信噪比的降低，RQA的参量：％recur，％determ，ratio，entropy和trends的绝对值呈下降的趋势．当SNR≥1000时，噪声对各参量的值影响不大．     

Recovering smooth dynamics from time series with the aid of recurrence plots

A graphical method based on recurrence plots is used in the reconstruction of the phase space from a time series of measurements. It is demonstrated that if the embedding delay and dimension are correctly chosen, the recurrence plot of a smooth dynamical system has a particularly simple form. It is shown how to use recurrence plots to determine the correct embedding parameters so that reliable quantitative information can be drawn about the system generating the time series. The average line length in the plot is shown to be directly related to the prediction horizon. Furthermore, it is a numerical characteristic of the embedded series independent of the threshold used in the plot.     

太阳高纬和低纬活动现象的混沌与分形特征

为了研究太阳高纬度和低纬度活动现象在南北半球的混沌与分形特征, 结合递归分析方法与Grassberger-Procaccia算法两种技术对1952年2月至1998年6月的极区光斑和黑子数目两种太阳磁活动指标进行了详细分析和比较. 主要结论如下: 1)由于太阳活动现象与磁场的时空演化密切相关, 导致太阳活动在南半球和北半球的混沌与分形特征具有不对称性, 太阳高纬度和低纬度活动现象的混沌与分形特征具有差异性; 2)太阳高纬度活动现象比低纬度活动现象具有更强的混沌程度和更复杂的分形结构, 其中太阳高纬度活动现象在北半球具有最强的混沌程度和最复杂的分形结构.     

基于复杂度的针刺脑电信号特征提取

为探究针灸刺激对大脑活动产生的影响,文章设计了4种针刺频率针刺右腿足三里穴获取脑电的实验.首次采用排序递归图和关联维数方法提取针刺脑电信号的复杂度参数来反映针刺大脑的功能状态,并基于这些方法研究了针刺作用对大脑功能区域的影响以及不同针刺频率与脑电复杂度的相关性.发现针刺时脑电的复杂度高于针刺前,尤以频率为100次/min的针刺影响最为明显;从FP2, F7, T3导联脑电中提取的确定性指标(DET)可作为区分针刺状态与针刺前状态的一种特征参数. 关键词： 针灸 脑电 排序递归图 关联维数     

Semiclassical Calculation of Recurrence Spectra of He Rydberg Atom in Strong External Fields

Using core-scattered closed-orbit theory and region-splitting iterative method, we calculated the scaled recurrence spectra of helium atom in parallel electric and magnetic fields. Closed orbits in the corresponding classical system have also been obtained. When we search the closed orbits, in order to remove the Coulomb singularity of the classical Hamiltonian motion equations, we implement the Kustaanheimo-Stiefel transformation, which transforms the system from a three-dimensional to a four-dimensional one. The Fourier transformed spectrum of helium atom has allowed direct comparison between peaks in such plot and the scaled action values of closed orbits. The results are compared with those of the hydrogen case, which shows that the core-scattered effects play an important role in the recurrence spectra of the multi-electron Rydberg atom.     

Semiclassical calculation of the recurrence spectra of He Rydberg atom in perpendicular electric and magnetic fields

Closed orbit theory is a semiclassical technique for explaining the spectra of Rydberg atoms in external fields. By developing the closed orbit theory from two degrees of freedom to three non-separable degrees of freedom, we calculated the recurrence spectra of He Rydberg atom in perpendicular electric and magnetic fields. The closed orbits in the corresponding classical system have also been obtained. Fourier transformed spectra of He atoms have allowed direct comparison between the resonance peaks and the scaled action values of closed orbits, whereas the nonhydrogenic resonance can be explained in terms of the new orbits created by the core scattering. The semiclassical result is in good agreement with the quantum spectra, which suggests that our method is correct.     

Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems

The three most widely used methods for reconstructing the underlying time series via the recurrence plots (RPs) of a dynamical system are compared with each other in this paper. We aim to reconstruct a toy series, a periodical series, a random series, and a chaotic series to compare the effectiveness of the most widely used typical methods in terms of signal correlation analysis. The application of the most effective algorithm to the typical chaotic Lorenz system verifies the correctness of such an effective algorithm. It is verified that, based on the unthresholded RPs, one can reconstruct the original attractor by choosing different RP thresholds based on the Hirata algorithm. It is shown that, in real applications, it is possible to reconstruct the underlying dynamics by using quite little information from observations of real dynamical systems. Moreover, rules of the threshold chosen in the algorithm are also suggested.     

Characterization of stickiness by means of recurrence

We propose recurrence plots (RPs) to characterize the stickiness of a typical area-preserving map with coexisting chaotic and regular orbits. The difference of the recurrence properties between quasiperiodic and chaotic orbits is revisited, which helps to understand the complex patterns of the corresponding RPs. Moreover, several measures from the recurrence quantification analysis are used to quantify these patterns. Among these measures, the recurrence rate, quantifying the percentage of black points in the plot, is applied to characterize the stickiness of a typical chaotic orbit. The advantage of the recurrence based method in comparison to other standard techniques is that it is possible to distinguish between quasiperiodic and chaotic orbits that are temporarily trapped in a sticky domain, from very short trajectories.     

Recurrence spectra of He atoms in strong external fields

1 Introduction The photo-absorption phenomenon of high Rydberg atoms in strong external fields has attracted much attention in recent years. The semiclassical closed-orbit theory[1,2] developed by Du and Delos has been extensively used to explain this phenomenon. This theory has successfully calculated and interpreted the photo-absorption spectra of H- in various external fields[3,4] and has been applied to describe the photo-excitation, wave packet dynamics of some atoms and molecules such…