一个新的超混沌系统设计与实现

在三阶Qi系统的基础上,构造了一个具有两个较大正的Lyapunov指数和较大参数范围新的超混沌系统,分析了该系统的平衡点及稳定性,Lyapunov指数谱和分形维数,超混沌吸引子的相图等特性,并利无量纲状态方程的模块化设计方法实现了该系统,实验结果与仿真结果完全一致。     

Design and experimental confirmation of a novel switched hyperchaotic system

To generate complex pseudo-noise (PN) sequences for chaos-based communications, this article presents a novel switched hyperchaotic model, which is constructed based on a modified Chen system by introducing a dynamical controller. The system consists of two different hyperchaotic subsystems and can change its behavior randomly via a switching function. Basic dynamical behaviors of the hyperchaotic system are further investigated. Furthermore, the switched system is confirmed by its positive Lyapunov exponents and laboratory measurements by an electronic circuit.     

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。     

基于双曲正切忆阻器的Duffing系统中簇发、共存分析及其DSP实现

忆阻器作为第4种基本电路元件由蔡少棠首次提出,它的提出为混沌电路的设计和工程应用提供了新思路。该文通过在Homles型Duffing系统中引入一个双曲正切忆阻模型,得到了一个新忆阻Duffing非自治系统。利用转换相图、相图、Lyapunov指数等,揭示了该系统具有振荡尖峰数目可控簇发、非完全对称双边簇发、非完全对称的簇发共存、多种周期混沌共存等新颖动力学行为。并通过分岔图及平衡点分析,研究了其簇发产生机理。采用Multisim电路仿真与数字信号处理平台(DSP)对系统进行了硬件实现,与理论分析基本一致的实验结果证明该系统是可行的且是物理可实现的。     

Discrete Chaos-I: Theory

We propose a definition of the discrete Lyapunov exponent for an arbitrary permutation of a finite lattice. For discrete-time dynamical systems, it measures the local (between neighboring points) average spreading of the system. We justify our definition by proving that, for large classes of chaotic maps, the corresponding discrete Lyapunov exponent approaches the largest Lyapunov exponent of a chaotic map when M/spl rarr//spl infin/, where M is the cardinality of the discrete phase space. In analogy with continuous systems, we say the system has discrete chaos if its discrete Lyapunov exponent tends to a positive number, when M/spl rarr//spl infin/. We present several examples to illustrate the concepts being introduced.     

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.     

Design of a tensile-type 3-D multi-scroll chaotic system and its application in secure communication

A kind of tensile-type 3-D multi-scroll chaotic attractor based on Chua's circuit was successfully designed. The chaos generation mechanism was studied by analyzing the symmetry and invariance, the existence of the dissipation, as well as the system equilibrium and stability. Then, some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic dynamical behaviors of the new chaotic system were introduced, either numerically or analytically. At the same time, the chaotic circuit of this system was realized by PSPICE. Finally, based on Lyapunov theorem and unidi-rectionally coupled method, the synchronization of the chaotic system has also been investigated. With this approach, the novel system can be applied to secure communication, which can achieve the purpose of covering specific signals. The experimental results are in agreement with numerical simulation results, which verifies the availability and feasibility of this method.     

一个具有无限多吸引子共存的新混沌系统的动力学分析及其电路实现

提出了一个新的具有超多稳定性的三维连续自治混沌系统,该系统仅有2个非线性项.对系统的耗散性、平衡点的稳定性进行了定量分析,并利用分岔图、Lyapunov指数、彭加莱截面和吸引子相图分析了系统参数以及初值对其动力学行为的影响.在参数固定的情况下,分析初值变化的分岔图,得到了无限多种共存吸引子.通过采用模拟开关电子元件设计实现了该系统,同时运用Multisim软件仿真了该系统的混沌电路.结论证明电路仿真与数值仿真结果一致.     

基于混沌、分形理论的多径衰落分析

本文首次将混沌、分形等非线性理论引入多径衰落的研究,针对现场实测数据分析了它的非线性动力特征.首先通过重构状态空间和关联维数验证了其动力机制的有限维自由度,然后通过计算其Lyapunov指数考察了系统的时空演化特性,最后利用分形机制对多径信号进行了重构.研究结果表明,与传统的随机模型相比,非线性动力模型能更恰当地描述多径衰落的内在物理机制.     

Chaos,intermittency and control of bifurcation in a ZC2-DPLL

Nonlinear dynamics of a dual sampler-based zero crossing digital phase lock loop (ZC₂-DPLL) has been investigated. Analysis supported by detailed numerical studies shows that the system enters a chaotic state through a cascade of period doubling bifurcation. The dynamics of the system have been quantified with the dynamical measures of Lyapunov exponent and correlation dimension. Further, it has been found that for certain system parameters intermittency occurs in the system. The occurrence of intermittency has been proved using the Pomeau–Manneville principle. The phenomenon of bifurcation control in a ZC₂-DPLL using time delay feedback has been explored. It has been found that for some suitably chosen control parameters bifurcation phenomena can be controlled such that the stable locked zone of a bifurcation controlled ZC₂-DPLL can be extended, which enhances the application potentiality of a ZC₂-DPLL.     

一个切换混沌系统的分析与电路实现

采用改变系统乘积项的方法,在已提出的混沌系统的基础上,构建了一个切换混沌系统。分析了平衡点的性质,混沌吸引子相图和Lyapunov指数等特性,设计了可实现切换混沌系统的电路并进行了电路实验,实现结果与仿真结果一致：     

Coexistence of infinite attractors in a fractional-order chaotic system with two nonlinear functions and its DSP implementation

In this paper, a new five-dimensional fractional-order chaotic system based on two nonlinear functions is constructed. The rich dynamical behaviors of the system are analyzed by phase diagram, bifurcation diagram and Lyapunov exponents spectrum. In addition, the complexity of the fractional-order system is analyzed through Spectral Entropy (SE) and Permutation Entropy (PE) algorithms. Meanwhile the phenomenon of coexisting infinite attractors is analyzed. Of particular concern is that the phenomenon of multi-state transition and intermittent oscillation chaos is found in this new chaotic system. Furthermore, the system is implemented on the DSP platform. To the best of the knowledge, these rich dynamical characteristics and complicated phenomena are of great reference value in chaotic image encryption and other fields.     

Chaos and bifurcation in a third-order digital phase-locked loop

Nonlinear dynamics of a third-order zero crossing digital phase locked loop (ZCDPLL) has been investigated. It has been observed that, while first and second-order ZCDPLLs show period doubling route to chaos, a third-order ZCDPLL manifests a disjoint periodic attractor in its route to chaos. Also, the complexity and predictability of the system dynamics have been characterized by using nonlinear dynamical measures such as Lyapunov exponent, Kaplan–York dimension, correlation dimension and Kolmogorov entropy. All the results show that the chaos in a third-order ZCDPLL is low dimensional.     

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。     

Weak signal detection and adaptive synchronous stability of a novel fifth-order memristive circuit system

This paper is devoted to introduce a novel complex fifth-order memristive circuit system and its applications in synchronous stability and weak signal detection. Firstly, the typical dynamical behaviors of the memristive system are discussed by chaotic phase portrait, complexity analysis, one-parameter bifurcation and Lyapunov exponent spectrum. Secondly, the adaptive control method is applied to realize the synchronization between the drive memristive system (DMS) and the response memristive system (RMS). The results indicate that the synchronization method has strong robustness and anti-interference ability. Thirdly, the weak signal detection of the novel five-dimensional memristive system is realized by using the extreme sensitivity of chaotic system to initial values. Finally, the fifth-order memristive circuit is designed by using basic electronic elements and simulated by Multisim software. And the anti-interference ability and sensitivity of the fifth-order memristive circuit are further verified by adding different weak disturbance signals at different positions of the circuit.     

Variable neural networks for adaptive control of nonlinear systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time, according to specified design strategies, so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive control scheme is presented. The location of the centers and the determination of the widths of the GRBFs in the variable neural network are analyzed to make a compromise between orthogonality and smoothness. The weight-adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modeling error(s). The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using two simulated examples     

Dynamic behavior analysis, color image encryption and circuit implementation of a novel complex memristive system

This paper is devoted to introduce a novel four-dimensional memristor-involved system and its applications in image encryption and chaotic circuit. The typical dynamical behaviors of the memristor-involved system are explored, such as chaotic phase potraits, Lyapunov exponent spectrum (LES), bifurcation diagram (BD) and complexity analysis. Then a color image encryption algorithm is designed. In this algorithm, the sequences generated by the four-dimensional memristor-involved system are used in scrambling and diffusion algorithm for three channels. The algorithm analysis results based on key space, key sensitivity, information entropy, histogram distribution, correlation coefficients, data loss and noise attacks indicate that the proposed algorithm can improve the security of the color image encryption algorithm. Finally, the memristor-involved chaotic circuit is implemented by using some discrete components. The experimental results of hardware circuit are consistent with the Multisim simulation results and the numerical simulation results. The research results have certain universality and portability, and can provide technical support for the subsequent analysis of other nonlinear circuits and the application of chaotic secure communication.     

具有时延的简单神经元模型的混沌行为

该文研究了具有时延的简单神经元方程周期解的失稳和混沌现象,数值仿真表明:在一阶非线性时延动力学系统中找到了新的混沌发生源,文中给出了例子的波形图、相图及最大Lyapunov指数图。     

一种变形Lorenz系统的混沌特性研究

在Lorenz混沌系统的基础上,加入周期策动力信号形成一种变形的Lorenz系统。利用广义哈密顿系统理论的梅尔尼科夫方法,证明变形Lorenz系统具有Smale马蹄变换意义下的混沌。利用功率谱、Lyapunov指数谱、庞卡莱映射等分析方法,进一步证明了变形Lorenz系统具有混沌系统的运动规律。变形Loren系统主要具有混沌态和类周期态两种状态。当系统处在一个临界状态,系统参数的微小变化就可以引起系统状态的性质变化,使最大Lyapunov指数由正变负。仿真实验表明该混沌系统对微弱周期信号非常敏感,同时对噪声具有极强的免疫力,这种性质使得混沌系统具有检测小信号的潜力,可以实现强噪声背景下弱周期信号有效的自动检测。变形Lorenz系统信噪比工作门限可达到-29dB,进一步优化系统参数,还可以继续降低信噪比下限。      

Detection of signals in chaos

In this paper, we present a new method for the detection of signals in “noise”, which is based on the premise that the “noise” is chaotic with at least one positive Lyapunov exponent. The method is naturally rooted in nonlinear dynamical systems and relies on neural networks for its implementation. We first present an introductory review of chaos. The subject matter selected for this part of the paper is written with emphasis on experimental studies of chaos using a time series. Specifically, we discuss the issues involved in the reconstruction of chaotic dynamics, attractor dimensions, and Lyapunov exponents. We describe procedures for the estimation of the correlation dimension and the largest Lyapunov exponent. The need for an adequate data length is stressed. In the second part of the paper we apply the chaos-based method to a difficult task: the radar detection of a small target in sea clutter