Analysis of quaternary digital chaotic sequence performance based on chaotic matrix

With good randomness and high sensitivity to initial values,chaotic sequences have been extensively used in secure communication.Real chaotic sequences are highly sensitive to initial values.It is an analog quantity in the domain of attraction,which is not conducive to the transmission of digital signals.In order to improve the stability,real chaotic sequences can be quantized into digital chaotic sequences.According to the relationship between the information rate and the symbol rate,the symbol rate of binary sequence is the same as the information rate.The information rate can be doubled by quantizing a real-valued sequence into a quaternary sequence.The chaotic sequence has weak periodicity.Moreover,the periodicity of binary digital chaotic sequences is much weaker than that of quaternary chaotic sequences.Compared with the multi-dimensional chaotic map,the one-dimensional chaotic map has small key space and low security.In this paper,a new real-valued chaotic sequence is generated based on the chaotic matrix method constructed by Logistic map and Kent map.Two quantization methods are used to digitize the real-valued chaotic sequence to obtain the quaternary digital chaotic sequence.Moreover,the randomness,the time series complexity and the correlation of the new quaternary chaotic sequence are compared and studied.The simulation results demonstrate that the quaternary digital chaotic sequence obtained by the chaotic matrix has good randomness and correlation.

Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

THE STATE SPACE RECONSTRUCTION TECHNOLOGY OF DIFFERENT KINDS OF CHAOTIC DATA OBTAINED FROM DYNAMICAL SYSTEM

Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.

A self-adaptive synchronization controller for Liu chaotic systems

A kind of synchronization controller for Liu chaotic systems whose nonlinear components are subject to Lipschitz condition was proposed. By using Lyapunov function and linear matrix inequality technique, a self-adaptive synchronization controller was constructed for Liu chaotic systems. There are two components of our derived synchronization controller: linear and nonlinear component. Linear component is composed of errors of the state variables between driving-systems and responding-stems, and nonlinear component is a self-adaptive synchronization controller. a proof was given for proving the feasibility of this method, and numerical simulations of Liu chaotic systems show its effectiveness. Furthermore, this method can be applied to other chaotic systems, such as Chen systems, Lorenz systems, Chua systems and Rssler systems,etc.

Robust Fractional-Order Proportional-Integral Observer for Synchronization of Chaotic Fractional-Order Systems

In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities(LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional(FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

H_∞ Synchronization of Chaotic Systems via Delayed Feedback Control

The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality （LMI）. A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.

Adaptive synchronization of different kinds of chaotic neural networks

The purpose of the paper is to present an adaptive control method for the synchronization of different classes of chaotic neural networks. A new sufficient condition for the global synchronization of two kinds of chaotic neural networks is derived. The proposed control method is efficient for implementing the synchronization when the parameters of the drive system are different from those of the response system. A numerical example is used to demonstrate the validity of the proposed method and the obtained result.

基于改进Logistic混沌和交叉混沌扩散的强鲁棒性图像加密

针对现有部分图像加密算法鲁棒性弱的问题,本文提出了一种基于改进Logistic混沌和交叉混沌序列扩散的强鲁棒性加密算法。首先,对Logistic一维混沌进行变换,构造出一种混沌序列分布更加随机的新混沌系统;然后,利用螺旋矩阵变换进行第一次置乱,利用明文的哈希值构造混沌的初始密钥,引入明文相关的两个数值val1和val2结合新混沌系统构造交叉混沌序列;接着对置乱后的序列进行交叉混沌的扩散。为克服螺旋矩阵变换部分像素未发生改变的问题,再进行一次交叉混沌置乱,形成置乱-扩散-置乱的加密框架。最后对本算法进行仿真模拟,其中本文密文图像的平均相关系数为–0.0027,更加趋近于0,大大的破坏了图像内部之间的相关性,达到图像加密的效果。像素变化率NPCR为99.61%,归一化强度UACI为33.36%,都分别接近于理想值99.60%和33.34%;密文图像的信息熵为7.9975,接近于理想值8,密钥的敏感性为10–17;能够在椒盐噪声和高斯噪声强度为0.2的情况下,仍然能够识别出解密图像。而且加密图像剪切1/2时,仍然能够恢复出明文图像;实验结果表明,本文算法具有较高的安全性,能够抵御选择明文攻击和穷举攻击,具有较强的抗噪声和抗剪切能力,对于图像传输过程中的安全性提供一定的保障,能够对于灰度图像达到安全稳定的加解密效果。

基于混沌粒子群优化算法的反应釜温度预测控制研究

反应釜作为化工行业核心的生产容器,其温度控制优化在化工生产领域中具有重要作用。针对反应釜温度控制难的问题,提出了一种基于Tent映射的混沌粒子群优化(CPSO)算法优化动态矩阵控制(DMC)-比例积分微分(PID)的反应釜温度预测控制策略。由于DMC很难选取较优的参数,利用Tent映射的CPSO算法提高动态矩阵参数寻优的速度。通过试验,以及与常规PID、DMC-PID控制对比分析,基于Tent映射的CPSO-DMC-PID串级控制对温度控制系统有较好的控制精度和响应速度,可大幅缩小超调量。该控制策略对反应釜温度预测控制研究具有一定的参考意义。

基于Kent混沌测量矩阵的压缩感知图像重构算法

图像重构是图像数字化和恢复高质量图像信号的关键技术,使用压缩感知理论进行图像重构的意义在于显著减少采样次数,降低系统资源的消耗。测量矩阵的构造是压缩感知的重要研究内容之一。提出一种基于Kent混沌测量矩阵的压缩感知图像重构算法,将Kent混沌序列作为测量矩阵,采用离散小波变换的稀疏化方法,在小波域对原始图像信号进行测量。最后采用正交匹配追踪方法恢复原始图像。仿真实验中,对比高斯随机测量矩阵和Logistic混沌测量矩阵,对不同的图像进行重构。实验结果证明,基于Kent混沌测量矩阵的重构算法能够恢复原始图像,重构性能优于高斯随机观测矩阵和Logistic混沌测量矩阵,同时克服了随机测量矩阵硬件难以实现的缺陷。

一种基于复合混沌映射的压缩感知测量矩阵构造方法研究

针对常用随机测量矩阵存在硬件实现困难的不足,提出一种基于复合混沌映射的压缩感知确定性测量矩阵构造方法.首先基于Logistic映射和Tent映射构造随机性和初值敏感性更强的复合混沌映射,然后将复合混沌迭代序列经大间隔采样后进行线性变换得到的结果作为拟构造测量矩阵中的元素,并从理论上证明了该矩阵元素具有非常低的相关性.同时理论证明了所构造复合混沌测量矩阵能以高概率满足压缩感知约束等距性.实验结果表明,所构造复合混沌测量矩阵的性能优于Toeplitz测量矩阵及Logistic映射测量矩阵,与高斯随机测量矩阵的性能相仿.

基于多组混沌序列的彩色数字图像置乱算法

传统的数字图像置乱算法需要多次迭代,加密强度不高,密钥空间小,抗攻击能力弱。针对上述问题,基于多组混沌序列和矩阵拉直算子,提出一种新的图像置乱算法。通过对彩色数字图像的RGB矩阵进行拉直和置乱,隐藏原始图像所含信息。理论分析和实验结果表明,该算法具有较大的密钥空间,对密钥敏感,能改变图像的灰度特征,且置乱后的图像纹理细、颗粒均匀。

经济混沌模型中一种改进的反馈控制方法

就经济系统中的一类多参数混沌模型 ,应用非线性动力学理论 ,在OGY方法的基础上 ,对反馈控制方法进行了改进 ,提出了基于预测的反馈控制方法 .该方法成功地进行了多参数混沌控制 ,并通过两例具体的经济混沌模型 。

并行定向扰动的混合粒子群优化算法

针对全向变异易使粒子失去已有的有利搜索信息的问题,提出了一种并行定向变异的混合粒子群优化算法。该算法以当前群体最优位置为基准,用变异信息矩阵和混沌位置变异矩阵对群体进行并行定向扰动,有效利用了现有的有利搜索信息。该算法将并行定向变异与序列二次规划法融为一体,实现了全局搜索和局部寻优的统一。仿真实验和比较分析结果表明并行定向变异混合粒子群优化算法具有良好的、稳定的优化效果。

基于神经网络混沌吸引子的公钥密码算法安全性分析及其实现

介绍一种基于神经网络混沌吸引子的Diffie-Hellman公钥密码算法.在过饱和贮存的Hopfield神经网络模型中混沌吸引子与初始状态之间存在一种单向函数关系,如果改变该神经网络的联结权矩阵,混沌吸引子及其所应的初始状态吸引域会随之发生改变.因此,我们可以其联结权矩阵为陷门,利用可交换的随机变换矩阵来改变神经网络的联结权矩阵,实现一种新的Diffie-Hellman公钥加密算法,即将随机变换矩阵作为私钥,而将变换后的神经网络联结突触矩阵作为公钥.为了说明这种新公钥加密方案的实用性,本文还分析和讨论其安全性和加密效率,并利用Java编程实现互联网的应用方案.实验结果表明,本算法是可行的,并具有较高的数据加密和解密速度.

基于循环移位和多混沌映射的图像加密算法

利用单一混沌系统实现的加密算法结构简单且容易被攻击,采用多个混沌系统加密是提高加密系统安全性的有效措施。文中提出一种基于循环移位和多混沌映射的图像加密算法,循环移位操作可以有效地改变图像的像素值。首先,利用分段线性混沌映射(Piecewise Linear Chaotic Map,PWLCM)和Logistic映射产生不同的混沌序列,并根据不同混沌序列生成索引矩阵和循环移位数。然后,根据索引矩阵对明文图像进行置换操作,根据循环移位数对置换图像依次做左循环移位操作。最后,通过Logistic混沌序列和PWLCM混沌序列对循环移位后的图像进行置乱和扩散操作,最终得到加密图像。对图像直方图、信息熵、差分攻击、相关性进行的测试和分析结果表明,所提加密算法具有高安全性和抵御各种攻击的能力,可以应用于图像加密系统中。

基于Logistic混沌序列的灰度图像加密算法

以混沌理论为基础,提出了一种灰度图像加密算法,该算法利用Logistic映射分别产生异或矩阵和置换矩阵,然后对灰度图像进行分块加密。实验仿真表明,该加密算法具有良好的加密效果。

一种新的基于神经网络混沌吸引子的公钥密码算法

论述了一种新的基于神经网络混沌吸引子的公钥密码算法,在过饱和贮存的Hopfield神经网络模型中混沌吸引子与初始状态之间存在一种单向函数关系,改变神经网络的联结权矩阵,混沌吸引子及其相应的吸引域会随之发生改变,如果以联结权矩阵为陷门,并利用可交换的随机变换矩阵来改变神经网络的联结权矩阵,则可以创建一种新的Diffie-Hellman公钥加密算法.将随机变换矩阵作为私钥,而将变换后的神经网络联结突触矩阵作为公钥,介绍了这种新的公钥加密方案,并分析和讨论其安全性和加密效率.

基于混沌序列的压缩感知测量矩阵构造算法

测量矩阵的构造算法是压缩感知中重要的研究方向之一。提出一种基于Logistic混沌一贝努利序列（Chaos．Bernoulli）测量矩阵构造算法，该算法利用了混沌序列良好的伪随机性质，通过一维Logistic混沌系统产生混沌序列，再通过符号函数生成具有贝努利分布的伪随机序列从而构造出压缩感知测量矩阵。实验仿真结果表明，该算法优于贝努利随机测量矩阵，信号重构的峰值信噪比PSNR有1～3dB的提高，并与其他类型的测量矩阵进行比较，数值分析结果证明该算法是可行有效的。

基于混沌Gyrator变换与矩阵分解的光学图像加密算法

为了解决当前光学图像加密技术没有考虑明文自身特性,使其抗明文攻击能力较低,且易增加密钥的分配与管理难度的问题,设计了基于混沌Gyrator变换与矩阵分解的非对称彩色图像加密算法。首先,从彩色图像中分别获取其R、G、B分量;设计二维耦合混沌系统,生成3个随机相位掩码,分别对R、G、B分量进行调制;基于卷积操作,将调制后的R、G、B分量融合为一幅灰度图像;利用混沌系统输出的随机序列来计算Gyrator机制的旋转角度,对灰度图像完成Gyrator变换,获取Gyrator频谱;根据相位-幅度截断机制,对Gyrator图像完成截断操作,形成幅度与相位信息;再引入一种矩阵分解机制,将相位截断图像分解为酉矩阵与三角矩阵,利用旋转角度不同的Gyrator变换分别处理酉矩阵与三角矩阵,完成图像加密。在图像加密过程中,利用其幅度截断图像信息来生成R、G、B分量的解密密钥,使得加密与解密密钥是截然不同的,只需利用私钥即可解密图像。测试数据表明,与较为主流的光学加密方案相比,所提技术具备更高的安全性,可有效抗击明文攻击。