一类新型超混沌系统的非线性反馈同步研究

一类由快变和慢变吸引子构成的新型超混沌系统,具有强的抗噪声能力,但是采用传统同步算法时,同步收敛速度较慢,同步性能对响应系统参数敏感。针对该问题,该文提出非线性反馈同步算法,根据Hurwitz稳定原理,设计非线性控制变量,使得误差方程雅可比矩阵的特征值实部均小于零,并使得特征值的绝对值较大。该算法比传统同步算法收敛速度快,并且具有对系统参数不敏感的优点。仿真结果验证了上述算法的有效性。     

一种双基地MIMO雷达快速多目标定位方法

该文研究了双基地MIMO雷达测向交叉多目标定位方法,提出了一种基于传播算子的双基地MIMO雷达快速多目标定位算法。该方法避免了一般子空间方法中占主要运算量的协方差矩阵估计和奇异值分解,不需要二维谱峰搜索,在保证二维方位角估计性能的基础上,降低了运算复杂度。利用矩阵的初等变换以及矩阵、矩阵特征值和特征值对应的特征向量三者之间的关系,该算法所估计二维方位角参数能自动配对,不需要额外的配对运算。最后仿真结果验证了该算法的有效性。     

基于FM合成的多算子反馈模型的乐音重塑

通过FM合成基本原理,建立乐音重塑算子模型。提出基于FM合成的多算子反馈模型算法。对算法应用快速傅里叶变换理论,将算法生成的数据映射到频域上,并进行频谱分析以及和标准A4音比对,从而验证重塑乐音的优劣性。实验讨论了有反馈和无反馈算法频谱的区别,通过贝塞尔函数建立反馈后音色频谱表达式,分析反馈算法在不同时隙上频谱变化对乐音合成的影响。通过调查人们对合成乐音的感受,从客观和主观上验证多算子模型的品质。最后提出一种最优多算子反馈模型算法,该算法具有很好的频谱特性和音乐和谐性,可通过该算子对乐音进行良好的重塑。     

一个恒定Lyapunov指数谱鲁棒混沌系统及其微控制器实现

在基本Sprott-B混沌系统数学模型的基础上,引入一个控制参数进行系统改造,构建出一个恒定Lyapunov指数谱鲁棒混沌系统。通过相轨图、Lyapunov指数谱和分岔图等动力学工具对系统进行了仿真分析。研究结果表明,系统对唯一的控制参数保持恒定的Lyapunov指数谱,从而工作于鲁棒混沌状态,理论分析则揭示出控制参数对于系统的混沌振荡具有线性或非线性调幅作用。此外,在以改进的Euler算法进行离散化后,采用微控制器MSP430F249进行了实验验证,证明了系统的可实现性。     

天波超视距雷达海杂波的混沌动态特性分析

利用替代数据法对实测回波信号进行非线性检验,Cao方法进行相空间重构、Rosenstein小数据量法计算最大Lyapunov指数、改进的格拉斯伯格-庞加莱算法(GPA)计算Kolmogorov熵以及局部可预测性检验研究了高频天波雷达(OTHR)海杂波的混沌动态特性。仿真计算表明:实测的高频天波雷达海杂波吸收子具有稳定收敛的关联维数、正的最大Lyapunov指数和正的Kolmogorov熵以及具有局部可预测的特性,验证了高频雷达海杂波确实来自于一个低维混沌系统。利用方差分析初步讨论了电离层对回波混沌特性的影响,研究表明:电离层将对回波混沌特性产生显著的影响。这些结论对高频雷达目标探测和海杂波建模研究都具有重要意义。     

基于指数-余弦离散混沌映射的图像加密算法研究

为了增强图像数据传输的安全性,该文提出一种新型的2维指数-余弦离散混沌映射系统。该系统通过向1维余弦混沌系统中引入指数和高次幂非线性项来构造新型混沌映射。引入的非线性项对1维余弦混沌系统的迭代过程进行扰动得到更饱满的混沌相轨。利用Lyapunov指数谱、系统分岔图等对该系统的混沌动力学性质进行了验证。基于此混沌映射,该文提出一种新型的混沌图像加密算法。该算法通过“置乱-扩散-置乱”等加密环节,使得加密后的数据具有很好的数据安全性。加密图像数据的安全性分析也表明2维指数-余弦混沌映射具有较强的算法鲁棒性以及加密安全性。     

基于非线性特征的表面肌电信号模式识别方法

该文提出一种计算非线性时间序列信号Lyapunov指数的新方法球均值Lyapunov指数计算法,用于肢体肌电信号的特征提取与分类。首先采用所提方法计算出肌电信号的Lyapunov指数,并与关联维组合构成输入特征向量,然后用二叉树法构造基于对支持向量机的多类分类器,对握拳、展拳、腕内旋、腕外旋4类动作模式进行分类识别。实验结果表明,该方法不仅具有比 Rosenstein 算法更强的抗干扰能力,而且在肌电信号的特征提取与分类应用中取得96.0%以上的识别率,适合于分析信噪比较低的混沌信号。     

基于传输矩阵的激光谐振腔模式计算

建立了激光谐振腔往返传输矩阵,通过求解往返传输矩阵的特征值与特征向量,获得了激光谐振腔模式特征.该方法可以用于快速计算同阶贝塞耳函数的所有谐振腔模式和衍射损耗,其结果与Fox-Li数值迭代方式计算结果完全一致.分别就对称谐振腔往返传输矩阵的A2与单程传输矩阵A的特征值及特征向量之间的关系和物理意义,以及非对称谐振腔往返传输矩阵AB与BA的特征值及特征向量之间关系和物理意义进行了分析和讨论,建立了数学表达式,并可以通过改变传输矩阵来提高计算效率.分析了对称共焦腔离散单元数量对光腔模式计算结果的影响,建立了最佳离散单元数量与谐振腔镜片半径的关系表达式,并实现了大菲涅耳系数共焦腔模式的计算.     

音频信号的混沌特性分析

依据非线性动力学理论,在音频信号的修正离散余弦变换(MDCT)域,采用自相关法和虚假近邻法(FNN)分别计算延迟时间和嵌入维数,重构出音频信号MDCT域信息的相空间,并基于Rosen-stein小数据量法计算最大Lyapunov(李雅普诺夫)指数,依据其正负对音频频域序列的混沌特性进行了统计分析和验证。实验表明,音频信号MDCT序列的最大Lyapunov指数皆为正,音频信号具有混沌特性。     

一种波达方向、频率联合估计快速算法

首先提出了基于PM(propagator method)方法的波达方向(DOA)、频率联合估计快速算法，给出了PM算子的一个估计，由PM算子构造出一特殊的低维矩阵，其特征值给出频率的估计，进而由估计的频率和相应的特征矢量得到DOA的估计。该算法具有参数自动配对，计算量小的优点，易于在工程应用中实时处理。计算机仿真结果证实了算法的有效性。     

一个一维离散混沌判定定理及其在伪随机数发生器中的应用

该文研究了一类取模运算的1维离散动力系统,提出了一个这类离散映射的混沌判据,利用Marotto定理证明了其混沌的存在性。给出了几个满足该判据的特殊形式的系统,分析了其分岔图、Lyapunov指数谱等基本动力学性质,通过模拟结果验证了理论的正确性。基于新系统设计了一个伪随机数发生器(PRNG), SP800-22随机性检测结果表明了该序列具有良好的伪随机性。进一步给出了一个图像加密方案,其密钥空间可以达到2747。该文提出的新系统的系统参数可以无穷多,所以理论上该加密方案的密钥空间可以无穷大。     

一类混沌电路的跃变参数识别与同步*

基于李亚普诺夫稳定性理论和矩阵理论,用两种方法对一类混沌电路系统参数发生跃变情况下的参数识别与同步控制进行了理论分析和数值计算机模拟。第一种方法是通过负反馈将系统镇定到某个稳定态来识别系统的跃变参数（系统参数突然发生阶跃性变化）,通过计算李亚普诺夫指数获得反馈系数临界值。第二种方法是基于李亚普诺夫稳定性理论得到的参数观测器包含了可调节的增益系数,当两个混沌系统达到完全同步时驱动系统的5个未知参数在阶跃变化情况下也可以被准确识别。最后对两种方法的优缺点进行了比较和分析。     

用李雅谱诺夫指数配置法控制统一混沌系统

解析设计控制器，通过配置相应的李雅谱诺夫指数，使统一混沌系统趋于预期点．由于受控后系统李雅谱诺夫指数具有先知性，因此，我们可以根据需要改变李雅谱诺夫指数的大小来控制系统收敛速度．设计还表明，受控的统一混沌系统的收敛情况与参数无关。     

Chaotic behavior of gastric migrating myoelectrical complex

Nonlinear feedback induces oscillation, whereas dynamic equilibrium between positive and negative nonlinear feedback generates rhythm. Physiological rhythms are central to life. No absolutely stable or periodic rhythm exists in living tissues. It has been extensively reported that many rhythms in human and animal organs, such as the heart and brain, are, in fact chaotic. The aim of this paper is to investigate whether the migrating myoelectrical complex (MMC) of the stomach was chaotic. The study was performed in eight healthy female hound dogs (15-22 kg), implanted with four pairs of bipolar electrodes on the serosa of the stomach along the greater curvature. After the dogs were completely recovered from the surgery, one complete cycle of gastric MMC was recorded from the serosal electrodes. Using Takens' embedding theorem, two parameters reflecting chaotic behavior, the attractor and the Lyapunov exponent of the myoelectrical recording, were reconstructed and computed, respectively. Statistical analysis was performed to investigate the difference in the Lyapunov exponents among different phases of the MMC. The results show that the MMC of the stomach is chaotic. Different phases of the MMC are characterized with different shapes of the attractors and different values of Lyapunov exponents. The characteristic chaotic behavior of the gastric MMC may be utilized for the identification of different phases.     

简并光学参量振荡器的同步研究

通过计算简并光学参量振荡器系统的李雅普诺夫指数,证明了该系统存在混沌和超混沌吸引子,即简并光学参量振荡器是混沌系统,并得到了系统处于混沌状态时的参数取值范围.进一步,利用反馈技术实现了简并光学参量振荡器的混沌同步和周期同步,给出了反馈控制的具体形式并进行了仿真计算,理论结果与数值仿真结果一致.     

Eigenvalues and eigenvectors of generalized DFT, generalized DHT,DCT-IV and DST-IV matrices

In this paper, the eigenvalues and eigenvectors of the generalized discrete Fourier transform (GDFT), the generalized discrete Hartley transform (GDHT), the type-IV discrete cosine transform (DCT-IV), and the type-IV discrete sine transform (DST-IV) matrices are investigated in a unified framework. First, the eigenvalues and their multiplicities of the GDFT matrix are determined, and the theory of commuting matrices is applied to find the real, symmetric, orthogonal eigenvectors set that constitutes the discrete counterpart of Hermite Gaussian function. Then, the results of the GDFT matrix and the relationships among these four unitary transforms are used to find the eigenproperties of the GDHT, DCT-IV, and DST-IV matrices. Finally, the fractional versions of these four transforms are defined, and an image watermarking scheme is proposed to demonstrate the effectiveness of fractional transforms     

Secure Communication via Synchronization of Lur’e Systems Using Sampled-Data Controller

In this paper, synchronization of chaotic Lur’e systems using sampled-data control is applied to the secure communication problem. The message is transmitted and masked by the techniques of n-cipher and a public key obtained by the chaotic Lur’e system. The decryption of the transmitted encrypted message to recover the original message at the receiver can be achieved by synchronizing the transmitter and receiver chaotic systems. Sampled-data feedback control is used for synchronization, and a sufficient condition for obtaining feedback gain is derived in terms of linear matrix inequalities using a discontinuous Lyapunov functional. The secure communication system is simulated via Matlab along with the Chua system to show the effectiveness of the proposed result.     

Three-Dimensional Chaotic Autonomous System with a Circular Equilibrium: Analysis,Circuit Implementation and Its Fractional-Order Form

A three-dimensional autonomous chaotic system with a circular equilibrium is investigated in this paper. Some dynamical properties and behaviors of this system are described in terms of equilibria, eigenvalue structures, bifurcation diagrams, Lyapunov exponents, time series and phase portraits. For specific parameters, the system displays periodic and chaotic attractors. The physical existence of the chaotic behavior found in the proposed system is verified by using the Orcad-PSpice software and experimental verification. A good qualitative agreement is shown between the experimental results, PSpice and numerical simulations. Furthermore, the commensurate fractional-order version of the system with a circular equilibrium is numerically studied. It is found that chaos exists in this system with order less than three. By tuning the commensurate fractional order, the system with a circular equilibrium displays chaotic and periodic attractors, respectively. Finally, chaos synchronization of identical fractional-order chaotic systems with a circular equilibrium is achieved by using the unidirectional linear error feedback coupling. It is shown that the fractional-order chaotic system can achieve synchronization for appropriate coupling strength.     

特征神经网络收敛性分析

求矩阵的特征值与特征向量的问题是科学和技术中广泛遇到的问题，本文将实对称矩阵的特征问题转化为求非线性方程的解的问题，并建立了一连续时间动力学神经网络来探讨该非线性方程，在相当一般的条件下利用Ｌｙａｐｕｎｏｖ函数讨论了网络的稳定性与收敛性。     

Adaptive Fuzzy Control of Nonlinear in Parameters Uncertain Chaotic Systems Using Improved Speed Gradient Method

This paper presents an adaptive fuzzy controller for Nonlinear in Parameters (NLP) chaotic systems with parametric uncertainties. In the proposed controller, the unknown parameters are estimated by the novel Improved Speed Gradient (ISG) method, which is a modification of Speed Gradient (SG) algorithm. ISG employs the Lagrangian of two suitable objective functionals for on-line estimation of system parameters. The most significant advantage of ISG is that it is applicable to NLP systems and it results in a faster rate of convergence for the estimated parameters than the SG method. Estimated parameters are used to design the fuzzy controller and to calculate the Lyapunov exponents of the chaotic system adaptively. Furthermore, established on the well-known Takagi–Sugeno (T-S) fuzzy model, a LMI (Linear Matrix Inequality)-based fuzzy controller is designed and is tuned using estimated parameters and Lyapunov exponents. Throughout the controller design procedure, several important issues in fuzzy control theory including relaxed stability analysis, control input performance specifications, and optimality are taken into account. Combination of ISG parameter estimation method and T-S-based fuzzy controller yields an adaptive fuzzy controller capable to suppress uncertainties in parameters and initial states of NLP chaotic systems. Finally, simulation results are provided to show the effectiveness of the ISG and adaptive fuzzy controller on chaotic Lorenz system and Duffing oscillator.