非线性动力系统分岔图中的暗线

基于非线性动力系统混沌运动的回归特性，构造了一种对分岔图中穿过混沌区的暗线进行研究的数值回归算法。运用该算法求得抛物线映射的暗线，并与通过暗线方程精确求得的暗线进行比较，验证了算法的有效性。对Brussel振子系统和分段线性单级齿轮动力系统的暗线进行了研究。通过对非线性动力系统分岔图中暗线的研究，由其切点可以得到嵌在混沌区中的周期窗口，由其交点可以得到混沌吸引子的激变点。研究结果表明该算法有助于分析系统的动力学行为和控制混沌运动。     

在中能重离子反应中核子的运动特征

在量子分子动力学模型框架下，研究了在中能重离子反应中单个核子的运动形态是规则的还是混沌的，它与反应系统的整体性质、反应机制是有关联的．在稳定的复合系统中，核子的运动显示出规则的行为．规则行为与混沌行为的并存反映了规则区域被不规则区域所包围的排斥极分岔特性，说明有中等质量碎片的局域稳定源存在．更多的不稳定轨道的出现则标志着这种局域稳定源的减少，有更多的核子及小集团发射．核子的混炖运动比核物质状态方程所标志的力学不稳定区域出现的时间更早．     

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     

毫米级高分辨率的混沌激光分布式光纤测温技术

近年来,随着分布式光纤传感技术在各大基础设施健康监测领域的广泛应用,人们对能够实现毫米量级精准定位和监测技术的需求日益增长.本文提出了一种基于宽线宽混沌激光的高分辨率分布式光纤测温技术.实验通过改变光反馈混沌源的偏振匹配态和反馈强度等外部参数,产生了–3 dB线宽约为7.5 GHz的宽线宽混沌激光,并在300 m传感光纤实现了空间分辨率为7.05 mm的分布式温度测量.同时,为了抑制光源线宽增加造成的布里渊增益谱恶化,在泵浦路中引入了时间门控技术,其中经脉冲调制后的泵浦光峰值功率提高了约9.5 dB,同时脉冲调制使混沌互相关锁定于脉冲持续时间内,从而布里渊增益谱的信号背景噪声比由约2.28 dB提升为4.55 dB,最终实现了空间分辨率为3.12 mm的分布式温度测量.     

Neural Volterra filter for chaotic time series prediction

A new second-order neural Volterra filter （SONVF） with conjugate gradient （CG） algorithm is proposed to predict chaotic time series based on phase space delay-coordinate reconstruction of chaotic dynamics system in this paper, where the neuron activation functions are introduced to constraint Volterra series terms for improving the nonlinear approximation of second-order Volterra filter （SOVF）. The SONVF with CG algorithm improves the accuracy of prediction without increasing the computation complexity. Meanwhile, the difficulty of neuron number determination does not exist here. Experimental results show that the proposed filter can predict chaotic time series effectively, and one-step and multi-step prediction performances are obviously superior to those of SOVF, which demonstrate that the proposed SONVF is feasible and effective.     

Parameter space map of an electron cyclotron resonance plasma in acompact chamber

Ion current density measurements were made in an electron cyclotron resonance (ECR) plasma reactor for both argon and oxygen discharges. Spatial changes in the ion current density were also recorded across the reactor diameter for changes in pressure and power. These measurements revealed a minimum in the ion current density on the reactor axis. This observation has been explained as a consequence of the shape of the ECR region, which, in turn, is dependent on the mode of coupling. Current density measurements were made as a function of reactor pressure and microwave power for two different axial locations in the system. A Langmuir probe was also used at these two locations to measure the electron temperature as a function of these process conditions. It was observed that the ion current density and/or plasma density measured downstream from the ECR zone, increased significantly in the low-pressure/high-microwave power region. Results from this region of the operating parameter space have not previously been reported. Further existing models do not predict this observed increase in plasma density or ion current density. It has been proposed that a rarefication of the gas in the ECR region, as a result of gas heating, has acted to increase the outward diffusion of electrons from the ECR zone and, thus, has increased the ambipolar diffusion of ions to the downstream location. This proposal has been partially validated by experimental results in which the ion energy was measured as a function of reactor pressure and gas flow rate. The shape of the oxygen parameter space map differs significantly from that for Ar. The principal reasons for these changes are a number of different inelastic electron scattering mechanisms which effect the transport electrons out of the ECR zone and through ambipolar diffusion also the transport of ions. The second factor is the production of negative ionic species which varies with reactor pressure and, thus, T_e     

An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps

The Lyapunov exponent is primarily used to quantify the chaos of a dynamical system. However, it is difficult to compute the Lyapunov exponent of dynamical systems from a time series. The entropic chaos degree is a criterion for quantifying chaos in dynamical systems through information dynamics, which is directly computable for any time series. However, it requires higher values than the Lyapunov exponent for any chaotic map. Therefore, the improved entropic chaos degree for a one-dimensional chaotic map under typical chaotic conditions was introduced to reduce the difference between the Lyapunov exponent and the entropic chaos degree. Moreover, the improved entropic chaos degree was extended for a multidimensional chaotic map. Recently, the author has shown that the extended entropic chaos degree takes the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. However, the author has assumed a value of infinity for some numbers, especially the number of mapping points. Nevertheless, in actual numerical computations, these numbers are treated as finite. This study proposes an improved calculation formula of the extended entropic chaos degree to obtain appropriate numerical computation results for two-dimensional chaotic maps.     

ORNL-HRIBF 6GHzECR离子源的最新结果

Experimental studies were conducted to characterize and improve the performance of the flat-B ECR ion source.The emittance of the source was investigated for the first time.The output beam currents of high-charge-states of Ar(q>8)were nearly doubled by increasing the plasma electrode aperture from 4mm to 6mm in diameter.To investigate possible enhancements with broadband microwave radiation,a"white"Gaussian noise generator was employed with a TWT amplifier to generate microwave radiation with a bandwidth of～200MHz.The performance of the flat-B ECR ion source was found to be much better with narrow bandwidth radiation when the source was operated in the flat-B region.However,the ion beam intensities and charge state distributions were improved with the broadband radiation when the source was tuned off the flat-B region.     

光与物质相互作用系统中的量子Fisher信息和自旋压缩

Fisher信息是估计理论中的重要概念,最近发现与量子信息中的纠缠判据具有密切联系.非旋波近似条件下,Dicke模型经典相空间表现为混沌动力学特征.本文详细考察了Dicke模型描述的光与物质相互作用系统中量子Fisher信息和自旋压缩动力学特性.结果表明:在短时瞬态情况下,无论初态处于规则区域还是混沌区域系统均表现为纠缠性质;但在长时稳态情况下,初态处于规则区域时系统纠缠消失,而初态处于混沌区域时系统则一直存在纠缠.通过与系统自旋压缩动力学性质相比较,发现量子Fisher信息可以更有效地刻画量子混沌.进一步考察初态处于规则和混沌区域时系统密度矩阵和纯度的动力学演化特性,发现混沌导致系统退相干现象发生,说明量子Fisher信息对混沌更敏感.     

基于在线误差修正自适应SVR的非线性不确定分数阶混沌系统滑模控制

提出了一种基于在线误差修正自适应SVR的滑模控制方法, 用于解决一类非线性不确定分数阶混沌系统的控制问题. 分别通过对混沌系统非线性函数的离线SVR估计和基于增量学习的状态跟踪误差在线SVR预测, 解决了不确定分数阶混沌系统模型难以预测的问题. 同时根据Lyapunov稳定性理论设计出SVR权值自适应调整律. 本文以分数阶Arneodo 系统为例进行仿真, 仿真结果表明了, 对于带有外界噪声扰动的非线性不确定分数阶混沌系统, 该方法可以在有限时间内将系统稳定至期望状态, 提高对非线性函数的预测精度, 改善控制性能.     

一个改进恒Lyapunov指数谱混沌系统的电路实现与同步控制

基于提出的恒Lyapunov指数谱混沌系统,通过将系统中的参数进行剥离,得到一个改进型的恒Lyapunov指数谱混沌系统.该混沌系统存在三个重要的特性：双参数恒Lyapunov指数谱、存在全局线性调幅参数和倒相参数.通过Lyapunov指数谱与分岔图结合理论证明与推理,揭示了该新系统存在的上述动力学特征.构建实验电路,实现了改进混沌系统,物理实验验证了新系统的混沌行为.最后,利用单变量反馈控制方法实现了新系统的同步控制,通过物理实验验证了新系统同步控制的条件. 关键词： 改进恒Lyapunov指数谱混沌系统 电路实现 同步控制     

ADDING ONE BIFURCATION IN A ROTOR SYSTEM WITH CLEARANCES

A mathematical model of a rotor system with clearances is analysed by the application of modern nonlinear dynamic theory. From the bifurcation diagrams, it is discovered that the rotor system alternates between periodic and chaotic motions at a supercritical rotational speed, and after undergoing a chaotic region the periodic number of the motion will increase by one. At the same time, the periodic number is equal correspondingly to the integral multiple of the critical rotational speed. At the subcritical rotational speed, it is discovered that the chaotic bands among successive orders of superharmonic responses return to the period one through a reversed period-doubling bifurcation, as a result of a period-doubling bifurcation. It is shown that the increase of damping may reduce the width of the chaotic bands and the amplitude of the periodic response; the increase of nonlinear degree also leads to the reduction of chaotic bandwidth, but makes the amplitude of the subharmonic response increase. So it is suggested that proper damping and correct material selection by considering the dynamic characteristics of the rotor system may reduce the proportion of faults and enhance the dynamic characteristics when designing the rotor system. The working speed should not be selected at N times its natural frequency and should not be set in the chaotic bands among the successive orders of periodic motion for the same purpose.     

Polarization-reversal-induced damping of left-hand polarized wave on electron cyclotron resonance

The left-hand polarized wave, which has been believed not to be related to electron cyclotron resonance (ECR), is for the first time demonstrated to be damped near the ECR point in an inhomogeneously magnetized plasma as a result of the polarization reversal to the right-hand polarized wave. The polarization reversal is found to be caused by the existence of the boundary between a plasma and a vacuum region, the local point of which shifts depending on the plasma column radius. This phenomenon is quantitatively explained in terms of the dispersion relation including the effect of the radial boundary condition.     

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.     

基于混沌理论和改进径向基函数神经网络的网络舆情预测方法

网络舆情发展趋势具有混沌系统的特征, 提出一种基于EMPSO-RBF神经网络的方法对网络舆情的发展趋势进行预测. 首先根据Lyapunov指数证明网络舆情具备混沌的特征, 然后对网络舆情时间序列数据进行相空间重构, 最后采用EMPSO-RBF方法进行预测, 并和其他模型进行对比试验, 实验结果表明EMPSO-RBF方法具有较高精确度.     

Chaotic wave trains in an oscillatory/excitable medium

We study the chaotic dynamics of a heterogeneous reaction–diffusion medium composed of two uniform regions: one oscillatory, and the other excitable. It is shown that, by altering the diffusion coefficient, local chaotic oscillations can be induced at the interface between regions, which in turn, generate different chaotic sequences of pulses traveling in the excitable region. We analyze the properties of the local chaotic driver, as well as the diffusion-induced transitions. A procedure based on the abnormal frequency-locking phenomenon is proposed for controlling such sequences. Relevance of the obtained results to cardiac dynamics is briefly discussed.     

CAPS satellite spread spectrum communication blind multi-user detecting system based on chaotic sequences

Multiple Path Interference (MPI) and Multiple Access Interference (MAI) are important factors that affect the performance of Chinese Area Positioning System (CAPS). These problems can be solved by using spreading sequences with ideal properties and multi-user detectors. Chaotic sequences based on Chebyshev map are studied and the satellite communication system model is set up to investigate the application of chaotic sequences for CAPS in this paper. Simulation results show that chaotic sequences have desirable correlation properties and it is easy to generate a large number of chaotic sequences with good security. It has great practical value to apply chaotic sequences to CAPS together with multi-user detecting technology and the system performance can be improved greatly. Supported by the National Basic Research Program of China (Grant No. 2007CB815500) and the National High Technology Research and Development Program of China (Grant No. 2007AA12z343)     

Nonlinear analysis using Lyapunov exponents in breast thermograms to identify abnormal lesions

Breast diseases are one of the major issues in women’s health today. Early detection of breast cancer plays a significant role in reducing the mortality rate. Breast thermography is a potential early detection method which is non-invasive, non-radiating, passive, fast, painless, low cost, risk free with no contact with the body. By identifying and removing malignant tumors in early stages before they metastasize and spread to neighboring regions, cancer threats can be minimized. Cancer is often characterized as a chaotic, poorly regulated growth. Cancerous cells, tumors, and vasculature defy have irregular shapes which have potential to be described by a nonlinear dynamical system. Chaotic time series can provide the tools necessary to generate the procedures to evaluate the nonlinear system. Computing Lyapunov exponents is thus a powerful means of quantifying the degree of the chaos.In this paper, we present a novel approach using nonlinear chaotic dynamical system theory for estimating Lyapunov exponents in establishing possible difference between malignant and benign patterns. In order to develop the algorithm, the first hottest regions of breast thermal images are identified first, and then one dimensional scalar time series is obtained in terms of the distance between each subsequent boundary contour points and the center of the mass of the first hottest region. In the next step, the embedding dimension is estimated, and by time delay embedding method, the phase space is reconstructed. In the last step, the Lyapunov exponents are computed to analyze normality or abnormality of the lesions. Positive Lyapunov exponents indicates abnormality while negative Lyapunov exponents represent normality. The normalized errors show the algorithm is satisfactorily, and provide a measure of chaos. It is shown that nonlinear analysis of breast thermograms using Lyapunov exponents may potentially capable of improving reliability of thermography in breast tumor detection as well as the possibility of differentiating between different classes of breast lesions.     

Sudden chaotic transitions in an optically injected semiconductor laser

We study sudden changes in the chaotic output of an optically injected semiconductor laser. For what is believed to be the first time in this system, we identify bifurcations that cause abrupt changes between different chaotic outputs, or even sudden jumps between chaotic and periodic output. These sudden chaotic transitions involve attractors that exist for large regions in parameter space.     

Theory of stability and bifurcation in a multi-quantum well laser with opto-electronic delayed feedback

This paper presents an opto-electronic feedback multi-quantum well laser system and outlines our study of the dynamics and bifurcation in a multi-quantum well laser due to the opto-electronic delayed feedback effect. We point out theoretically the conditions of stability and Hopf bifurcation of the laser. The relaxation oscillation frequency of the system is educed to be the function of the feedback level, delayed time and in-current. The route from stability to bifurcation is numerically simulated via varying the delayed time, feedback strength and in-current. The results show that the induced dynamics can be grouped into four distinct types or modes (stable, periodic pulsed, undamped oscillating or beating, and chaos), where the frequency and intensity varying with the delayed time in the two periodic regions are analyzed detailedly to find that the pulsing frequency is reduced with the long delayed time while the pulsing intensity is added with the long delayed time. And the chaotic pulsing frequency is increased with the large in-current. In addition, the carrier transport between the barrier region and the active region can characterize the dynamics in the laser to produce stable, periodic pulsed, beating and chaotic states by altering the carriers transport or escape rate value.