On-Off Intermittency Route to Chaos Synchronization and Spatial Periodic Synchronization of Chaos in Coupled Arrays of Chaotic Systems

Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We find that chaos synchronization in circular arrays of chaotic systems can occur through the on off intermittent synchronization with a power law distribution of laminar phases. And in the coupled ring and linear array it is found that the chaotic rotating waves generated from the ring propagate with spatial periodic synchronization along the linear array.

Circuit implementation and multiform intermittency in a hyper-chaotic model extended from the Lorenz system

This paper presents a non-autonomous hyper-chaotic system, which is formed by adding a periodic driving signal to a four-dimensional chaotic model extended from the Lorenz system. The resulting non-autonomous hyper-chaotic system can display any dynamic behaviour among the periodic orbits, intermittency, chaos and hyper-chaos by controlling the frequency of the periodic signal. The phenomenon has been well demonstrated by numerical simulations, bifurcation analysis and electronic circuit realization. Moreover, the system is concrete evidence for the presence of Pomeau- Manneville Type-I intermittency and crisis-induced intermittency. The emergence of a different type of intermittency is similarly subjected to the frequency of periodic forcing. By statistical analysis, power scaling laws consisting in different intermittency are obtained for the lifetime in the laminar state between burst states.

Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows

The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high- order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investi- gated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity （ESS） method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This valida~ tion provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.

High-Order Spectral Stochastic Finite Element Analysis of Stochastic Elliptical Partial Differential Equations

This study presents an experiment of improving the performance of spectral stochastic finite element method using high-order elements. This experiment is implemented through a two-dimensional spectral stochastic finite element formulation of an elliptic partial differential equation having stochastic coefficients. Deriving this spectral stochastic finite element formulation couples a two-dimensional deterministic finite element formulation of an elliptic partial differential equation with generalized polynomial chaos expansions of stochastic coefficients. Further inspection of the performance of resulting spectral stochastic finite element formulation with adopting linear and quadratic (9-node or 8-node) quadrilateral elements finds that more accurate standard deviations of unknowns are surprisingly predicted using quadratic quadrilateral elements, especially under high autocorrelation function values of stochastic coefficients. In addition, creating spectral stochastic finite element results using quadratic quadrilateral elements is not unacceptably time-consuming. Therefore, this study concludes that adopting high-order elements can be a lower-cost method to improve the performance of spectral stochastic finite element method.

Rucklidge-based memristive chaotic system:Dynamic analysis and image encryption

A new four-dimensional(4D)memristive chaotic system is obtained by introducing a memristor into the Rucklidge chaotic system,and a detailed dynamic analysis of the system is performed.The sensitivity of the system to parameters allows it obtains 16 different attractors by changing only one parameter.The various transient behaviors and excellent spectral entropy and C0 complexity values of the system can also reflect the high complexity of the system.A circuit is designed and verified the feasibility of the system from the physical level.Finally,the system is applied to image encryption,and the security of the encryption system is analyzed from multiple aspects,providing a reference for the application of such memristive chaotic systems.

SPECIAL DYNAMIC BEHAVIORS OF A TEMPORAL CHAOTIC SYSTEM

When dynamic behaviors of temporal chaotic system are analyzed, we find that a temporal chaotic system has not only generic dynamic behaviors of chaotic reflection, but also has phenomena influencing two chaotic attractors by original values. Along with the system parameters changing to certain value, the system will appear a break in chaotic region, and jump to another orbit of attractors. When it is opposite that the system parameters change direction, the temporal chaotic system appears complicated chaotic behaviors.

Dynamical analysis,circuit realization,and application in pseudorandom number generators of a fractional-order laser chaotic system

A new five-dimensional fractional-order laser chaotic system(FOLCS)is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system.Dynamical behavior of the system,circuit realization and application in pseudorandom number generators are studied.Many types of multi-stable states are discovered in the system.Interestingly,there are two types of state transition phenomena in the system,one is the chaotic state degenerates to a periodical state,and the other is the intermittent chaotic oscillation.In addition,the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm.Moreover,a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit.Finally,a pseudo-random sequence generator is designed using the FOLCS,and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22.This study enriches the research on the dynamics and applications of FOLCS.

面向物联网的多协议僵尸网络检测方法

针对现有僵尸网络检测方法采样不均、特征选择差、泛化能力较弱,导致检测分类效果偏低且对计算和存储资源受限的物联网环境的适应性较差等不足,本文提出了一种面向物联网的多协议僵尸网络检测方法 .通过所设计的基于地址三元组和时间窗口的IP聚合与特征重构方法整合从物联网网关中获取的网络流量,得到重构样本集.采用所提出的自修正混合加权采样算法平衡重构样本集中正常流量与僵尸流量,得到重采样样本集.采用所提出的基于多属性决策和邻接关系链的序列前向选择算法剔除重采样样本集中的冗余特征,得到最优特征子集.采用所设计的基于阵发混沌的秃鹰搜索算法优化后的两阶段混合异构模型,对经最优特征子集筛选后的重采样样本集进行检测分类.实验结果表明,所提方法对僵尸网络的检测效果较好,检测准确率为99.24%,马修斯相关系数为98.49%,误报率为0.17%,漏报率为1.29%,优于现有方法 .该方法能够有效降低采样与特征选择的时空开销,可较好地适应资源受限的物联网环境.

基于案例推理的极端天气下风功率预测系统研究

提高风功率预测精度是保障风电并网安全运行的关键,同时也是电力市场现货交易决策制定的支撑,而间歇性、波动性风速是影响风功率预测精度的重要因素。提出了一种基于案例推理的极端天气下风功率预测方法,首先利用混沌理论建立间歇性风速模型,进而确定极端天气预测案例库,其次建立基于案例推理的风功率预测模型,最后结合山西省大同市某风电场的实际运行数据进行验证,并与广义回归神经网络(GRNN)、最小二乘支持向量机(LSSVM)和遗传BP神经网络(GABP)三种方法的预测结果进行对比。仿真结果表明,该方法能够有效提升风电功率预测精度,或可为极端天气时的风功率预测研究提供借鉴。

基于频闪映射的Boost PFC变换器中的间歇性分岔和混沌现象分析

该文推导出了一组频闪映射方程来精确描述峰值电流控制型 Boost PFC 变换器的非线性动力学特性。数值模拟发现了系统电流在输入电压周期内会出现间歇性分岔和混沌现象,并对这种间歇性分岔和混沌的周期性进行了分析。通过对系统占空比的详细研究,发现系统并没有经过倍周期分岔的充分发展到达混沌,而是在倍周期分岔的过程中,发生边界碰撞分岔后以非光滑的方式直接进入混沌的。最后,给出了在输入电压幅值、参考电压和负载变化下系统的稳定域。这些结果对实际电路的设计具有重要的参考价值。

杜芬振子阵列实现弱正弦信号频率检测

杜芬振子从混沌到间歇性混沌的相变对与参考信号频差较小的周期小信号具有敏感性,而对白噪声和与参考信号频差较大的周期干扰信号具有免疫力。通过实验仿真,得出单个杜芬振子的信号检测范围。提出利用杜芬振子阵列检测微弱正弦信号的模型,实现微弱正弦信号的频率检测。

基于混沌理论的微弱信号检测方法

分析了间歇混沌模型———Duffing振子的混沌特性,利用Duffing振子的非平衡相变对微小信号具有敏感性及对白噪声和与参考信号频差较大的周期干扰信号具有免疫力的性质,采用混沌振子阵列实现对噪声背景下微弱信号的检测;并采用梅尔尼科夫方法作为混沌判据,该方法的优点在于可以直接进行解析计算。仿真实验表明:该检测方法简单、有效,检测的精度比较高。

齿轮故障的混沌诊断识别方法

研究了Ｈｏｌｍ ｅｓ型Ｄｕｆｆｉｎｇ 振子的混沌及间歇混沌运动，发现参考信号与摄动信号间的微小角频率差是振子产生间歇混沌的原因。得出振子相变对与参考信号具有微小角频率差的小信号敏感，而对随机噪声和与参考信号角频率差较大的周期干扰信号具有免疫力的结论。通过辨别振子对的间歇混沌运动可对齿轮偏心及单齿缺陷故障进行诊断与识别。

弱信号检测的混沌模型及应用

本文给出了一种典型的间歇混沌模型—— Duffing混沌振子 ,并详细的分析了其间歇混沌特性 .基于混沌现象发生随模型参数变化的间歇性 ,设计了噪声背景下弱信号的检测方案 .

基于混沌振子的低信噪比语音端点检测新方法

Duffing振子相变对与参考信号频差较小的周期小信号具有敏感性,对白噪声和与参考信号频差较大的周期干扰信号具有免疫力。利用语音的准周期性提出了一种基于混沌理论的语音端点检测新算法,讨论了如何利用Duffing振子的间歇混沌特性来检测语音端点。将含噪语音作为Duffing振子的外部参考信号的摄动,根据系统相图是否改变来检测语音段和噪声段。通过尺度变换并设计了振子阵列以检测频率范围较大的语音信号。实验结果表明,基于混沌的语音端点检测算法在低信噪比下明显优于传统的能量语音端点检测法。

一种新型频率测量方法的研究

研究了一种带摄动的Duffing振子混沌数学模型,详细的分析了其间歇混沌特性。根据Duffing振子对噪声的免疫力,提出了一种新型的频率测量方法,并给出了具体的算法。仿真结果表明,在强噪声背景下,该方法可以准确的测出微弱正弦信号的频率。

高阶开关功率变换器中的间歇现象

以四阶电流模式控制单端初级电感变换器(single ended primary inductor converter,SEPIC)为例,研究高阶开关功率变换器中的间歇混沌和间歇分谐波现象。从电路耦合滤波的角度考虑,建立具有耦合干扰信号的SEPIC变换器模型,通过数值仿真和电路仿真观察到了间歇现象,分析不同电路参数对干扰信号强度阈值的影响。并将时间分岔映射为参数分岔,继而以此为基础运用特征值分析方法对变换器的稳定性进行了分析。参数分岔图、特征值轨迹与时间分岔图完全一致,均表明干扰信号的强度和频率决定着间歇现象的类型和间歇周期的大小。

基于Hilbert变换及间歇混沌的水声微弱信号检测方法研究

利用Duffing振子从混沌到间歇混沌的相变及其对策动力和待检测信号频差较小的周期信号的敏感性,研究了强海洋背景噪声下微弱周期信号的检测.通过构造混沌振子列的方法对频率未知信号进行扫频,从而提取待检测信号的频率范围,最后利用希尔伯特变换,实现对间歇混沌的包络检测,并计算出待检测信号的频率.计算机仿真与实测水声信号处理结果表明,利用基于希尔伯特变换的间歇混沌振子对水声微弱信号检测,其检测信噪比比一般的间歇混沌振子提高了至少4.4 dB,验证了所提方法的有效性.

基于双Duffing振子差分的微弱信号频率检测

利用混沌振子检测微弱信号幅值需要先确定待测信号频率。本文在间歇混沌的基础上采用双振子差分方法构建振子阵列检测信号频率,将驱动力频率公比由1.03提高到1.06。计算机仿真实验证明该方法可以提高检测的带宽,减小计算量,降低误判几率。

Duffing振子信号探测在故障电弧短路保护中的应用

Duffing振子信号检测技术利用混沌系统的分岔特性来检测外界信号,将待测信号作为Duffing方程周期策动力的摄动,利用初值敏感性可以获得很高的测量灵敏度和良好的抗噪性能。基于Duffing振子信号检测技术提出一种新型的故障电弧监测方法。在电弧没有发生燃弧之前有比较微弱的弧声信号,完全湮没在强背景噪声中,将含有噪声的弧声信号作为周期策动力加入混沌检测系统中,如果混沌检测系统处于间歇混沌状态,证明有电弧弧声产生,则故障电弧监测系统发出预警信号。实验表明,发生燃弧的瞬间,弧光、短路电流、弧声的幅值都有明显的跃变,以这3个电弧表征信息为判据,设定合适的幅值阈值,建立报警系统。实验结果表明该监测系统能实现对故障电弧的预警和报警功能。