Adaptive synchronization of GLHS with unknown parameters

In this paper, an adaptive controller for the synchronization of two generalized Lorenz hyperchaos systems (GLHSs) is designed by using the Lyapunov method. In the synchronization schema, the parameters of the drive system are unknown and different from those of the response system. By introducing update laws for both the control coefficients and the parameters of the response system, the adaptive controller proposed in this paper is brand new compared with the former relative works. The proposed adaptive controller is feasible for any possible parameters of GLHS. Numerical simulation is carried out to verify and illustrate the analytical result. Copyright © 2008 John Wiley & Sons, Ltd.     

Hyperchaos of higher order and its circuit implementation

Though numerous hyperchaotic systems are reported, few of them can generate hyperchaotic attractors with more than three positive Lyapunov exponents. A new hyperchaotic system, constructed by adding the approximate time‐delayed state feedback to Chen system, is presented in this paper. This system has ring architecture with Chen system and several all‐pass filters coupled. With the increase of the number of all‐pass filters used in this system, the number of positive Lyapunov exponents also increases steadily. Hyperchaos of order 11 can be generated by this system. The resulting system is demonstrated by computer simulations and confirmed by an electronic circuit. Copyright © 2009 John Wiley & Sons, Ltd.     

Hyperchaos from two coupled Wien‐bridge oscillators

This paper proposes a simple inductorless approach to generating hyperchaos by coupling two Wien‐bridge oscillators with a resistor and a diode. The whole circuit is investigated both numerically and experimentally. Also, its hyperchaotic dynamics is studied theoretically by a topological horseshoe with two‐directional expansions which provides an immediate evidence of hyperchaos. Copyright © 2007 John Wiley & Sons, Ltd.     

一个超混沌系统的设计与电路实现

为了提高超混沌系统的随机性以产生复杂的超混沌信号用于混沌保密通信,通过在一个统一混沌系统中引入一个状态反馈控制器设计一个超混沌系统.利用理论和数值仿真的方法对系统的基本特性,如平衡点及在平衡点的特征值、分形维数、分岔图、Lyapunov指数等进行分析.为验证该系统,利用系统方法设计一个模拟超混沌电路.该设计方法重新标度时间和坐标变量,将状态方程变换为一个无量纲的标准方程,获得了一个确定电路参数的严格公式.实验中观察到了超混沌、混沌、拟周期、周期等动力行为,实验结果与数值仿真结果完全相符.     

A new hyperchaotic Lorenz‐type system: Generation,analysis, and implementation

A new four‐dimensional continuous‐time autonomous hyperchaotic Lorenz‐type system is introduced and analyzed. This hyperchaotic system is not only visualized by computer simulation but also verified with bifurcation analysis and realized with an electronic circuit. Moreover, explicit formulae for estimating the ultimate bound and positive invariant set of the system are derived by constructing a family of generalized Lyapunov functions. The findings and results of this paper have good potential in control and synchronization of hyperchaos and their engineering applications. Copyright © 2010 John Wiley & Sons, Ltd.     

基于Lorenz三维混沌序列的彩色图像加密算法

讨论了一种基于Lorenz混沌动力系统的三维彩色图像加密的算法。该算法首先对Lorenz系统输出的实值混沌序列进行预处理,然后根据序列随机修改图像中每一个像素点的RGB值,并对修改后的图像进行像素置乱。仿真与讨论结果表明,该算法密钥空间大,混沌信号的产生极其敏感地依赖于密钥,具有较好的加密效果和加密效率,并对统计分析具有较好的安全性。     

基于LabVIEW技术的Lorenz方程虚拟混沌信号发生器设计

利用美国NI公司的虚拟仪器软件LabVIEW设计混沌信号发生器。本文结合三阶非线性Lorenz方程理论用LabVIEW强大的数学分析功能编写混沌信号生成程序,进而由LabVIEW驱动数据采集卡输出混沌信号。与传统的自治混沌系统相比,此发生器具有参数调节方便、易实现、可靠度高等优点。     

Design and circuit implementation of a five‐dimensional hyperchaotic system with linear parameter

Based on an existing 4‐dimensional Lorenz hyperchaotic system, a novel 5‐dimensional hyperchaotic system is proposed by an extra linear control coefficient in this paper. Some related characters are analysed comprehensively, including the stability of equilibrium, dissipativity, rotation symmetry, bifurcations, Lyapunov exponent, and Poincare surface of a section of the hyperchaotic system. The 5‐dimensional hyperchaotic system is then implemented and simulated in the circuit simulation software NI Multisim. The results indicate that the proposed hyperchaotic system exhibits hyperchaos, chaos, and quasi‐periodic and periodic dynamic behaviours, which can facilitate and enhance the security of chaos‐based communication.     

A twin‐star hyperchaotic attractor and its circuit implementation

A very simple 4D system with a twin‐star hyperchaotic attractor is presented in this letter. Computer simulation is given to visualize the attractor, and a simple circuitry is designed for system implementation. Copyright © 2003 John Wiley & Sons, Ltd.     

采用模糊控制实现混沌系统的广义投影同步

研究了离散混沌系统的广义投影同步问题.基于Takagi-Sugeno(TS)模糊动态模型和Lyapunov稳定性理论,导出了离散混沌系统广义投影同步的一个充分条件.通过一些矩阵操作技巧,这个准则被转化为一组线性矩阵不等式形式.然后,这些线性矩阵不等式的求解可以用Matlab工具箱方便地解决.对Henon映射的数值模拟,仿真结果表明该方法的有效性.     

Control and synchronization of the generalized Lorenz system with mismatched uncertainties using backstepping technique and time‐delay estimation

We propose a robust control technique for regulation and synchronization of the generalized Lorenz system (GLS) that covers the Lorenz system, Chen system and Lü system. The proposed control provides synergy through the combination of the backstepping control and time‐delay estimation (TDE) technique. TDE is used to estimate and cancel nonlinearities and uncertainties while the backstepping method is adopted to provide robustness against matched and mismatched uncertainties. As a result, we observe in numerical simulation that the proposed technique shows better performances in regulating and synchronizing the GLS with mismatched uncertainties, in comparison with existing schemes. The efficacy of the proposed technique is also validated with a circuit‐implemented chaotic system. Copyright © 2017 John Wiley & Sons, Ltd.     

Adaptive fuzzy sliding mode control of Lorenz chaotic system

By using the exponential reaching law technology, a sliding mode controller was designed for Lorenz chaotic system subject to an unknown external disturbance. On this basis, considering the unknown disturbance, an adaptive law was introduced to adaptively estimate the parameters of the disturbance bounds. Furthermore, to eliminate the chattering resulting from the discontinuous switch controller and to guarantee system transient performance, a new adaptive fuzzy sliding mode controller was designed. The results of the simulation show the effectiveness of the proposed control scheme. Translated from Journal of Harbin Institute of Technology, 2006, 38(4): 499–502 [译自: 哈尔滨工业大学学报]     

混合编程在Lorenz混沌系统动力学行为仿真中应用

Lorenz混沌系统的动力学行为是由控制参数决定。以Lorenz混沌系统的动力学行为为实例,采用更加直观的相图和时域图并借助于Lab VIEW与MATLAB软件对之进行仿真,实现系统的动力学行为。分析了Lab VIEW与MATLAB两种编程语言的特点和混合编程技术,采用两者混合编程技术实现了有效仿真,给出了混合编程的具体实现过程。实践证明,Lab VIEW与MATLAB的结合运用,简单可行,相互补充,有利于程序的仿真,提高编程效率。     

The design and implementation of a multi‐wing chaotic attractor based on a five‐term three‐dimension system

The last two decades have seen great progress about the generation and circuit realization of multi‐wing chaotic attractor. In this paper, several multi‐scroll chaotic attractors are generated from a five‐term system by adding a piecewise linear function. Moreover, some basic properties in terms of symmetry and dissipation, equilibrium points, eigenvalues of the Jacobian matrices, Lyapunov exponent spectrum, bifurcation diagram, and Poincaré map are studied. In particular, an analog circuit is designed to implement the proposed multi‐scroll attractors, which are different from the traditional attractors. Furthermore, an integrated circuit diagram is designed to realize the fractional‐order multi‐scroll attractors. Finally, the performed experimental results confirm the theoretical analysis, and our work lends itself to many potential applications in engineering. Copyright © 2015 John Wiley & Sons, Ltd.     

Generating 2n‐wing attractors from Lorenz‐like systems

In this paper, the existence of 2n‐wing chaotic attractors in a family of Lorenz‐like systems is confirmed by both numerical simulation and circuit realization. By replacing a nonlinear cross‐product or square term in an original Lorenz‐like system with a newly designed multi‐segment quadratic function, multi‐wing attractor can be generated. The main design idea is to increase the number of index‐2 equilibrium points of the system. This approach can not only generate multi‐wing attractors in different Lorenz‐like systems, but can also allow the flexibility in specifying a precise number of wings to be created. Copyright © 2008 John Wiley & Sons, Ltd.     

The realization of inverse system for circuits containing nullors with applications in chaos synchronization

A very simple method for synthesizing the inverse system of a non-linear non-autonomous circuit containing nullors is proposed. The main application of the procedure is the synchronization of chaos by the inverse system approach. This is illustrated with two examples: the synchronization of a Duffing circuit and a communication scheme by direct chaotic modulation using Chua's circuit. © 1998 John Wiley & Sons, Ltd.     

Real‐time chaotic circuit stabilization via inverse optimal control

In this paper, an efficient approach is developed for real‐time global asymptotic stabilization of the chaotic Chen's circuit, as a typical example for chaotic circuit control. Based on a recently introduced methodology of inverse optimal control for nonlinear systems, a very simple stabilization control law, a linear state feedback, is electronically implemented for the desired global asymptotic stabilization. Both Chen's chaotic system and the designed controller are synthesized and realized by analog electronic components, with the aim of evaluating the physical performance of the real‐time control law and demonstrating the practicality of the control method, which is robust to some input uncertainties. Copyright © 2008 John Wiley & Sons, Ltd.     

多变量系统的广义预测控制解耦设计

针对双输入双输出机炉协调控制系统,首先将系统分解为两个双输入单输出系统,并用广义预测控制原理设计控制器,通过求解二元一次矩阵方程组,实现了多频预测的解耦控制。进行了仿真研究,仿真结果证实了算法的有效性。     

混沌保密通信实验电路设计

针对通信的安全可靠问题,探讨了利用混沌进行保密通信的可行性。根据Pecora和Carroll提出的驱动一响应同步方法,分析了蔡氏混沌电路的同步原理,设计了混沌掩盖通信的实验电路,给出了元件参数和波形。实验结果表明：当f≥8kHz时,输入方渡信号被掩盖传输,实现了混沌保密通信。     

Josephson结电路系统的混沌控制

本文在考虑隧道效应的前提下,分析了含Josephson结电路系统的复杂非线性动力学,建立了系统的非线性动力学方程。根据系统的相图、分叉图及Lyapunov指数图分析了系统由周期运动进入混沌运动的过程。利用外加耦合控制器和利用非线性状态反馈反馈法两种方法实NT系统混沌运动的周期控制,得到了受控系统的周期运动相图及混沌控制控制参数变化时的分叉图。并讨论了这两种控制方法的特点。