Relaxation and localization in interacting quantum maps

Quantum relaxation is studied in coupled quantum baker's maps. The classical systems are exactly solvable Kolmogorov systems, for which the exponential decay to equilibrium is known. They model the fundamental processes of transport in classically chaotic phase space. The quantum systems, in the absence of global symmetry, show a marked saturation in the level of transport, as the suppression of diffusion in the quantum kicked rotor, and eigenfunction localization in the position basis. In the presence of a global symmetry we study another model that has classically an identical decay to equilibrium, but-quantally shows resonant transport, no saturation, and large fluctuations around equilibrium. We generalize the quantization to finite multibaker maps. As a byproduct we introduce some simple models of quantal tunneling between classically chaotic regions of phase space.     

Gradient method for blind chaotic signal separation based on proliferation exponent

A new method to perform blind separation of chaotic signals is articulated in this paper, which takes advantage of the underlying features in the phase space for identifying various chaotic sources. Without incorporating any prior information about the source equations, the proposed algorithm can not only separate the mixed signals in just a few iterations, but also outperforms the fast independent component analysis(FastICA) method when noise contamination is considerable.     

指向Lyapunov指数及其在单输入单输出系统故障检测中的应用

针对单输入单输出系统的故障检测, 采用混沌振荡器作为激励源, 并利用非一致延迟时间法对被测系统输出时间序列进行相空间重构. 在相空间中平衡点附近定义了指向Lyapunov指数, 并用其对被测系统输出在相空间中平衡点附近特征结构进行分析, 实现了对单输入单输出系统的故障检测. 仿真结果表明, 被测系统的参数变化将会引起相空间中平衡点附近特征结构的改变, 指向Lyapunov指数对其变化敏感. 关键词： 混沌激励 指向Lyapunov指数 故障检测 单输入单输出系统     

基于独立成分分析和经验模态分解的混沌信号降噪

基于经验模态分解和独立成分分析去噪的特点,提出了一种联合独立成分分析和经验模态分解的混沌信号降噪方法. 利用经验模态分解对混沌信号进行分解,根据平移不变经验模态分解的思想构造多维输入向量, 通过所构造的多维输入向量和独立成分分析对混沌信号的各层内蕴模态函数进行自适应去噪处理; 将处理后的所有内蕴模态函数进行累加重构,从而得到降噪后的混沌信号. 仿真实验中分别对叠加不同强度高斯噪声的Lorenz混沌信号及实际观测的月太阳黑子混沌序列进行了研究, 结果表明本文方法能够对混沌信号进行有效的降噪,而且能够较好地校正相空间中点的位置, 逼近真实的混沌吸引子轨迹. 关键词： 独立成分分析 经验模态分解 混沌信号 降噪     

基于最大Lyapunov指数不变性的混沌时间序列噪声水平估计

提出了一种基于最大Lyapunov指数不变性的计算混沌时间序列噪声水平的新方法. 首先分析了噪声对相空间中两点距离的影响, 然后基于最大Lyapunov指数在不同维数的嵌入相空间不变的性质, 建立了估计噪声水平的方法. 仿真计算结果表明, 当噪声水平小于10% 时, 估计值与真实值符合良好. 该方法对噪声分布类型不敏感, 是一种有效的混沌时间序列噪声估计方法.     

Application of local polynomial estimation in suppressing strong chaotic noise

In this paper, we propose a new method that combines chaotic series phase space reconstruction and local polynomial estimation to solve the problem of suppressing strong chaotic noise. First, chaotic noise time series are reconstructed to obtain multivariate time series according to Takens delay embedding theorem. Then the chaotic noise is estimated accurately using local polynomial estimation method. After chaotic noise is separated from observation signal, we can get the estimation of the useful signal. This local polynomial estimation method can combine the advantages of local and global law. Finally, it makes the estimation more exactly and we can calculate the formula of mean square error theoretically. The simulation results show that the method is effective for the suppression of strong chaotic noise when the signal to interference ratio is low.     

基于反馈和多最小二乘支持向量机的分数阶混沌系统控制

根据分数阶线性系统的稳定理论,将混沌系统分成稳定的线性部分和相应的非线性部分.设计主动控制器,对非线性部分进行补偿,从而将分数阶混沌系统控制到平衡点.为了提高主动控制器的补偿能力,提出基于反馈的多最小二乘支持向量机(M-LS-SVM)拟合模型.通过减聚类方法将输入空间划分为一些小的局部空间,在每个局部空间中用LS-SVM建立子模型.为解决子模型相互之间的严重相关问题,提高模型的精度和鲁棒性,各个子模型的预测输出通过主元递归(PCR)方法连接.仿真实验表明该方法有助于提高补偿精度和系统响应指标. 关键词： 分数阶 混沌系统 多最小二乘支持向量机 反馈     

一种基于人工蜂群算法的混沌信号盲分离方法

混沌信号所固有的非周期、宽带频谱和对初值极度敏感等特性使得对这类信号进行盲分离极为困难. 针对这一问题, 提出一种新的盲分离方法, 该方法通过相空间重构来构造代价函数, 将混沌信号的盲分离转化为一个无约束优化问题, 并利用人工蜂群算法进行求解. 不同于现有的独立成分分析方法仅使用混合信号的统计特性来解决分离问题, 该方法能充分利用混合信号内在的动态特性, 因而在处理混沌信号这种确定性信号时能获得更好的分离效果. 此外, 正交矩阵的参数化表示有效地降低了盲分离问题的复杂性, 使优化过程能快速收敛. 实验结果表明, 该方法具有较快的收敛速度和较高的数值精度, 在分离混沌信号时其整体性能优于现有的几种盲分离方法. 同时, 在分离混沌-高斯混合信号的实验中该方法也展现出优异良好的性能, 这表明该文的方法有应用潜力.     

谐和激励与有界噪声作用下具有同宿和异宿轨道的Duffing振子的混沌运动

研究了具有同宿轨道、异宿轨道的双势阱Duffing振子在谐和激励与有界噪声摄动下的混沌运动.基于同宿分叉和异宿分叉，由Melnikov理论推导了系统出现混沌运动的必要条件及出现分形边界的充分条件.结果表明：当Wiener过程的强度参数大于某一临界值时，噪声增大了诱发混沌运动的有界噪声的临界幅值，相应地缩小了参数空间的混沌域，且产生混沌运动的临界幅值随着噪声强度的增大而增大.同时数值计算了最大Lyapunov指数，由最大Lyapunov指数为零从另一角度得到了系统出现混沌运动的有界噪声的临界幅值，发现在Wi 关键词： 混沌 同宿和异宿分叉 随机Melnikov方法 最大Lyapunov指数     

Nonlinear Dynamics and Fluctuations of Dissipative Toda Chains

The dynamics of a ring of masses including dissipative forces (passive or active friction) and Toda interactions between the masses is investigated. The characteristic attractor structure and the influence of noise by coupling to a heat bath are studied. The system may be driven from the thermodynamic equilibrium to far from equilibrium states by including negative friction. We show, that over-critical pumping with free energy may lead to a partition of the phase space into attractor regions corresponding to several types of collective motions including uniform rotations, one- and multiple soliton-like excitations and relative oscillations. The distribution functions in the phase space and the correlation functions of the forces and the spectra of nonlinear excitations are calculated. We show that a finite-size Toda ring with weak thermal coupling develops at intermediate temperatures a broadband colored noise spectrum with an 1/f tail at low frequencies.     

微波管中离子张弛振荡的混沌现象

微波管中离子张弛振荡引起的噪声对其工作性能有很大影响，已成为微波管领域研究的焦点之一.用包络方程描述电子束特性，用离散的宏粒子模型描述离子特性，在此基础上编写了一维粒子模拟程序，对行波管与速调管模拟，得到张弛振荡的时间序列；将振荡看作是一个复杂非线性动力学系统的响应，分析了离子张弛振荡时间序列的功率谱、重构相图及Lyapunov指数，指出离子张弛振荡具有混沌性质，为研究离子张弛振荡的控制与带有离子振荡噪声信号的处理提供了参考. 关键词： 张弛振荡 粒子模拟 微波管 混沌     

混沌背景中微弱信号检测的神经网络方法

基于复杂非线性系统相空间重构理论，提出了混沌背景中微弱信号检测的神经网络方法，利用神经网络强大的学习和非线性处理能力，建立了混沌背景噪声的一步预测模型，从预测误差中检测淹没在混沌背景噪声中的微弱目标信号(包括周期信号和瞬态信号)，研究了混沌背景中存在白噪声时该方法的检测能力，指出了目标信号为瞬态信号和周期信号时检测原理的异同点，最后以Lorenz系统作为混沌背景噪声进行了仿真实验，实验表明该方法能有效地将混沌背景中极其微弱的信号检测出来. 关键词： 混沌 神经网络 信号检测     

Lorenz系统长程相关性研究

以典型的混沌系统——Lorenz系统为研究对象,运用去趋势涨落分析方法对不同初值和不同参数条件下系统的长程相关性进行研究.结果表明：系统长程相关性与系统初值所处相空间位置有关,初值越靠近不稳定平衡点,系统长程相关性越强,其标度指数α就越大,系统可预测性也就越好.当系统完全处于混沌状态时,随着控制参数r逐步增大其动力学结构的混沌特性更加明显,标度指数α都呈下降趋势,系统长程相关性逐渐减弱,系统可预测性也随之减弱.这揭示了长程相关性与系统可预测性的对应关系.对系统进行 关键词： Lorenz系统 长程相关性 去趋势涨落分析 可预测性     

Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise

An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator driven by weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase sensitivity of the oscillator and the correlation function of the noise, and are explicitly calculated for oscillators with sinusoidal phase sensitivity functions driven by two typical colored Gaussian processes. The results are verified by numerical simulations using several types of stochastic or chaotic noise. The drift and diffusion coefficients of oscillators driven by chaotic noise exhibit anomalous dependence on the oscillator frequency, reflecting the peculiar power spectrum of the chaotic noise.     

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.     

Spin dynamics and spin noise in the presence of randomly varying spin-orbit interaction in a semiconductor quantum wire

Using ensemble Monte Carlo simulation, we have studied hot carrier spin dynamics and spin noise in a multi-subband GaAs quantum wire in the presence of a randomly varying Rashba spin-orbit interaction. The random variation reduces the carrier ensemble's spin dephasing time due to the D'yakonov-Perel' mechanism, but otherwise makes no qualitative difference to the temporal spin relaxation characteristics. However, it makes a qualitative difference to the spatial spin relaxation characteristics which change from monotonic and smooth to non-monotonic and chaotic because of a complex interplay between carriers in different subbands. As far as spin fluctuation and spin noise are concerned, the random variation has no major effect except that the low-frequency noise power spectral density increases slightly when the magnitude of the Rashba spin-orbit interaction field is varied randomly while holding the direction constant.     

一类多涡卷混沌系统构造方法研究

提出一种基于平移变换的多涡卷混沌系统构造方法.首先选取合适的不稳定线性系统,利用一系列相互平行的分界面对相空间进行划分,然后通过对该线性系统进行平移变换,使新系统作用于相应的空间区域,最后利用基于符号函数的非线性函数来统一表示整个系统.根据该方法可以构造具有任意奇数个涡卷的新型混沌系统,同时也可以对某些现有混沌系统进行改进,使之成为多涡卷系统.数值仿真结果验证了该方法的可行性. 关键词： 多涡卷混沌吸引子 平移变换 涡卷     

Coarse grained variables and deterministic chaos in an excitable system

Temporal coarse graining was applied to the dynamical variables of a semiconductor laser with optical feedback. The chaotic low frequency fluctuations obtained in numerical and experimental data are shown to have properties of a self-excitable deterministic system. External exciting noise is replaced by the ultrafast chaotic oscillations of the system. A low dimensional coarse-grained phase space is defined and time constants are introduced and measured for the exponential drop and recovery of the randomly excited equally shaped spikes.     

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．