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.     

基于视觉辐条图案识别方法的蓝宝石引晶机制研究

工业生产蓝宝石晶体过程中,引晶步骤有着至关重要的地位。引晶必须在温度梯度较小,温度分布趋于稳定的条件下进行。目前,工业生产蓝宝石主要依靠人工经验操控籽晶杆实现引晶操作,但是人工引晶操作的准确性不高会导致成品品质不佳、资源浪费。为此,本文提出一种基于蓝宝石视觉辐条图案识别方法来检测蓝宝石熔体状态自由液面状态,从而实现一种高效率引晶的机制。此方法利用经典骨架化算法细化辐条图案,Harris算子实现特征信息的提取,提取的特征信息放入运动轨迹模型中判断熔体稳定性,分析液面温度分布稳定性从而实现引晶。结果表明,此算法具有有效性,蓝宝石晶体引晶效率大大提高,生产出的成品良率也有提升,可有效指导蓝宝石的工业生产。     

Concurrence and Quantum Discord in the Eigenstates of Chaotic and Integrable Spin Chains

There has been some substantial research about the connections between quantum chaos and quantum correlations in many-body systems. This paper discusses a specific aspect of correlations in chaotic spin models, through concurrence (CC) and quantum discord (QD). Numerical results obtained in the quantum chaos regime and in the integrable regime of spin-1/2 chains are compared. The CC and QD between nearest-neighbor pairs of spins are calculated for all energy eigenstates. The results show that, depending on whether the system is in a chaotic or integrable regime, the distribution of CC and QD are markedly different. On the other hand, in the integrable regime, states with the largest CC and QD are found in the middle of the spectrum, in the chaotic regime, the states with the strongest correlations are found at low and high energies at the edges of spectrum. Finite-size effects are analyzed, and some of the results are discussed in the light of the eigenstate thermalization hypothesis.     

基于图像重组和比特置乱的多图像加密

针对现有多图像加密算法只能同时加密多张同类型同大小的图像,适用范围不广、实用性差等问题,提出一种基于图像重组和比特置乱的多图像加密算法.该算法通过将任意数量、不同大小和不同类型的图像重新组合成新多灰度图,一次完成同时加密,极大提高了加密效率和适用范围.首先,依次提取所有待加密图像像素值重新组合出N张m×n新灰度图,并将其转化成m×n×8N二进制矩阵.然后,采用3D比特置乱方式,对高位页进行行列比特置乱,低位页进行整页比特置乱.最后,进行异或扩散操作,得到密文图像.高低位分开置乱提高了算法的抗噪声能力,最终密文信息熵达到7.999以上,很好地掩盖了明文的统计特性.构造一种新型Logistic与广义三阶Fibonacci级联的混沌系统产生随机序列,增加了初值和控制参数范围,扩大了密钥空间,使其达到8×10^84以上,极大地提高了抗穷举攻击能力.既提高了序列随机性,又同时保留了低维混沌系统的快速性.结合明文哈希值(SHA-256)产生密钥,明文像素值发生微小改变后密文像素值变化率达到0.996以上,极大地提高了的明文敏感性和算法抗选择明文攻击的能力.实验分析表明,提出的多图像加密算法安全性高、实用性强.     

An Improved Composite Multiscale Fuzzy Entropy for Feature Extraction of MI-EEG

Motor Imagery Electroencephalography (MI-EEG) has shown good prospects in neurorehabilitation, and the entropy-based nonlinear dynamic methods have been successfully applied to feature extraction of MI-EEG. Especially based on Multiscale Fuzzy Entropy (MFE), the fuzzy entropies of the τ coarse-grained sequences in τ scale are calculated and averaged to develop the Composite MFE (CMFE) with more feature information. However, the coarse-grained process fails to match the nonstationary characteristic of MI-EEG by a mean filtering algorithm. In this paper, CMFE is improved by assigning the different weight factors to the different sample points in the coarse-grained process, i.e., using the weighted mean filters instead of the original mean filters, which is conductive to signal filtering and feature extraction, and the resulting personalized Weighted CMFE (WCMFE) is more suitable to represent the nonstationary MI-EEG for different subjects. All the WCMFEs of multi-channel MI-EEG are fused in serial to construct the feature vector, which is evaluated by a back-propagation neural network. Based on a public dataset, extensive experiments are conducted, yielding a relatively higher classification accuracy by WCMFE, and the statistical significance is examined by two-sample t-test. The results suggest that WCMFE is superior to the other entropy-based and traditional feature extraction methods.     

Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.     

稳定分层湍流中逆梯度输运的关联分析研究

本文采用关联分析方法研究了稳定温度分层湍流中的结构特性、输运特性，以及热量、动量逆梯度输运现象的尺度效应及其参数演化．首先采用大涡模拟方法对稳定分层湍流中的结构特性和输运特性进行了分析，将逆梯度输运发生的时间尺度作为已知条件，结合关联量分析方法在波数空间中的解析解，对逆梯度输运现象的尺度效应进行了分析研究．结果发现，稳定分层强度较大的流动中发生垂向热量及动量逆梯度输运现象，发生的结构尺度与关联分析所发现垂向热量、动量逆梯度输运的波数形成了呼应．随着分层强度增加，热量、动量的输运强度均受抑制，与逆梯度输运关联的流场结构尺度减小，同样的效应也发生在流场结构向下游演化的过程中．     

Delay driven Hopf bifurcation and chaos in a diffusive toxin producing phytoplankton‐zooplankton model

This paper deals with a diffusive toxin producing phytoplankton‐zooplankton model with maturation delay. By analyzing eigenvalues of the characteristic equation associated with delay parameter, the stability of the positive equilibrium and the existence of Hopf bifurcation are studied. Explicit results are derived for the properties of bifurcating periodic solutions by means of the normal form theory and the center manifold reduction for partial functional differential equations. Numerical simulations not only agree with the theoretical analysis but also exhibit the complex behaviors such as the period‐3, 5, 6, 7, 8, 11, and 12 solutions, cascade of period‐doubling bifurcation in period‐2, 4, quasi‐periodic solutions, and chaos. The key observation is that time delay may control harmful algae blooms (HABs). Moreover, numerical simulations show that the chaotic states induced by the period‐doubling bifurcation are purely temporal, which is stationary in space and oscillatory in time. The investigations may provide some new insights on harmful phytoplankton blooms.     

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.