Chen''''s混沌动力系统的控制

为了研究Chen’s混沌动力系统的混沌控制问题，通过双线性反馈方法将混沌控制在不稳定的平衡点，给出了非反馈周期信号控制混沌系统在不稳定周期轨道上（UPO）的方法。应用Lyapunov定理和Routh-Hurwitz判据分析了被控系统的稳定条件，数字仿真结果证明了控制方法的正确性、有效性。给出了控制Chen’s混沌动力系统到每一个平衡点的具体方法和稳定条件，得出了运用周期信号控制Chen’s混沌动力系统到高周期轨道的判定方法，解决了Chen’s混沌动力系统的控制问题。     

存在扰动的永磁同步电机混沌运动模糊自适应同步

电机的混沌运动并不总是有害的,在某种特殊应用场合中永磁同步电机的混沌运动是有益的,因此需要对永磁同步电机的混沌运动进行反控制.提出了一种存在扰动的永磁同步电机(PMSM)混沌运动的模糊自适应同步控制方法.分析了PMSM混沌运动的吸引子和lyapunov指数谱,使模糊控制规则满足系统的lyapunov稳定条件,设计模糊自适应控制器对存在扰动的PMSM混沌系统进行同步控制,仿真结果表明该方法可实现PMSM混沌运动的同步控制,具有较好的控制效果.     

基于图像识别理论的混沌特性判别方法

利用混沌振子可以检测微弱的周期信号，并且具有很多优点。该文针对Duffing混沌振子在信号检测领域中的应用，提出了基于图像识别理论的混沌特性判别方法。该方法具有直观、算法简单及计算量小的优点。文中阐述了所提方法的原理，并给出了相应的判别程序流程图及仿真实验结果。仿真结果表明，利用该方法可以准确快速地判断混沌特性，并能很好地满足Duffing混沌振子信号检测的需要。将该文提出的判别方法用于处理小电流单相接地故障保护的现场试验数据，获得了好的效果。     

存在扰动的永磁同步电机混沌运动模糊自适应同步

电机的混沌运动并不总是有害的,在某种特殊应用场合中永磁同步电机的混沌运动是有益的,因此需要对永磁同步电机的混沌运动进行反控制。提出了一种存在扰动的永磁同步电机（PMSM）混沌运动的模糊自适应同步控制方法。分析了PMSM混沌运动的吸引子和lyapunov指数谱,使模糊控制规则满足系统的lyapunov稳定条件,设计模糊自适应控制器对存在扰动的PMSM混沌系统进行同步控制,仿真结果表明该方法可实现PMSM混沌运动的同步控制,具有较好的控制效果。     

基于非线性反馈方法的连续时间稳定线性系统的混沌反控制

提出了连续时间线性稳定系统跟踪任意混沌系统实现混沌化的一般方法，该控制器通过非线性反馈取得，其中的反馈增益矩阵的求取与所跟踪的混沌系统无关，只与原连续时间线性稳定系统的状态矩阵有关。通过跟踪Rossler混沌系统和Lorenz混沌系统说明了该方法的设计过程。仿真结果表明了该方法的有效性和快速性。     

基于忆阻器的van der Pol混沌系统的线性反馈同步控制

基于忆阻器的van der Pol混沌系统的混沌特性,采用了线性反馈同步的控制方法,给出了基于忆阻器的van der Pol混沌系统实现同步的控制参数的取值范围,并通过数值仿真论证了该方法的可行性。     

分数阶Lorenz超混沌系统及其电路仿真

在Lorenz超混沌系统的基础上提出了分数阶超混沌系统,通过数值仿真、研究了系统的基本动力学特性,分析了在不同参数条件下的吸引子相图。设计了硬件电路并运用EWB软件对该电路进行仿真,电路仿真说明分数阶电路是可以实现的。     

连续时间线性稳定系统的混沌反控制

针对连续时间线性稳定系统跟踪任意混沌系统的实现方法，基于自适应控制策略，设计了自适应控制器，使连续时间线性稳定系统的动态轨迹跟踪任意给定的混沌系统的动态轨迹，从而实现连续时间线性稳定系统的混沌化，并基于Lyapunov稳定性理论，证明了自适应控制器设计的正确性。以二阶连续时间线性稳定系统跟踪Duffing混沌系统和三阶连续时间线性稳定系统跟踪Lorenz混沌系统为例，说明了该方法的设计过程。仿真结果表明了该方法的有效性。     

具有传输通道时间延迟的一类混沌系统脉冲控制同步

针对一类混沌系统同步控制问题,利用脉冲微分方程的稳定理论,研究了传榆信号具有时间延迟的混沌系统脉冲同步问题,给出了两个混沌系统实现全局渐进同步的判据方法。该方法仅采用具有时间延迟的驱动系统与响应系统输出偏差的线性反馈作为脉冲控制信号,驱动两个混沌系统达到全局渐进同步,且适用于绝大多数混沌系统的同步控制。所设计的控制器结构简单,收敛速度快,易于实现。Roessler混沌系统的仿真实验进一步验证了该方法的有效性和可行性。     

一类电机系统的混沌分析及电路实现

针对无刷直流电机开环系统等效非线性数学模型,运用混沌分析的方法对其存在的混沌现象进行了理论分析和仿真实验,确定了混沌系统的对称性、平衡点稳定性等相关理论问题,揭示了无刷直流电机系统通往混沌之路,并设计出与混沌数学模型相应的模拟电子电路,由虚拟示波器显示对应的电路运行状态图验证了该理论研究,进一步为无刷直流电机的混沌分析...     

四维超混沌系统及其在信号加密中的应用

为获得复杂的混沌信号源,构建四维超混沌系统,同时提出一种基于该系统的信号加密算法.构建系统模型,得到该系统的Lyapunov指数,给出了系统的相轨迹图,实现电路及该实现电路的相轨迹图;依据混沌隐藏技术,将该四维超混沌系统作为混沌加密通信的信号源,把待加密的信号与混沌信号相叠加,再把迭代次数与混沌信号的算术运算相结合作为密码设置,以实现信号加密.仿真结果表明,实现电路的相轨迹图与系统的相轨迹图完全一致,证实所构建的电路系统为超混沌系统,且该系统可以作为混沌加密通信的信号源实现对信号进行加密,为信息加密提供了一种新方法.     

Hyperchaotic behaviour of two bi‐directionally coupled Chua's circuits

In this paper, a non‐linear bi‐directional coupling of two Chua's circuits is presented. The coupling is obtained by using polynomial functions that are symmetric with respect to the state variables of the two Chua's circuits. Both a transverse and a tangent system are studied to ensure a global validity of the results in the state space. First, it is shown that the transverse system is an autonomous Chua's circuit, which directly allows the evaluation of the conditions on its chaotic behaviour, i.e. the absence of synchronization between the coupled circuits. Moreover, it is demonstrated that the tangent system is also a Chua's circuit, forced by the transverse system; therefore, its dynamics is ruled by a time‐dependent equation. Thus, the calculus of conditional Lyapunov exponents is necessary in order to exclude antisynchronization along the tangent manifold. The properties of the transverse and tangent systems simplify the study of the coupled Chua's circuits and the determination of the conditions on their hyperchaotic behaviour. In particular, it is shown that hyperchaotic behaviour occurs for proper values of the coupling strength between the two Chua's circuits. Finally, numerical examples are given and discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

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 new six-dimensional hyperchaotic system and its secure communication circuit implementation

In the paper, a novel six-dimensional hyperchaotic system is proposed for secure communication. A detailed analysis of some relevant features, such as equilibrium stability, dissipation, bifurcation, and Lyapunov exponents. The results show that there are hyperchaos, chaos, quasi-periodic, and periodic dynamic behaviors for our constructed hyperchaotic system. Then the six-dimensional hyperchaotic system is simulated and implemented, which verified its physical realizability. The six-dimensional hyperchaotic system is applied to complete the signal encryption and decryption circuit design, then the circuit is tested. The results indicate that the proposed hyperchaotic system can play an important role in some key areas such as communication security and complex systems.     

利用状态观测器实现四涡卷超混沌同步保密通信

根据系统的稳定性理论,设计了实现超混沌完全同步的状态观测器。利用混沌之间的同步,构建了实现保密通信的技术路线。信号经过加密并被混沌掩盖后,发射给接收端。采用4阶Runge—Kutta方法,对提出的保密通信系统进行了数值仿真。仿真结果显示,超混沌系统和其同步接收器之间在5S内已实现了完全同步,在信道内传递的加密信号中,原始信号完全被混沌所掩盖,仿真结果证实了设计方案的有效性。     

采用混沌振子和新相态判别法的局部放电检测

为了降低信号检测的信噪比,利用新型混沌振子作为检测工具,采用Lyapunov指数法分析动力学特性,通过提升临界混沌阈值精度减少在覆盖初始相位差方面混沌振子的使用数量。针对各主要相态判别方法的局限性,利用系统周期特点提出新相态判别法并设计仿真电路,实现相态的自动识别并记录间歇混沌状态周期。最后对单指数衰减振荡型局部放电信号进行检测。仿真结果表明,新型混沌振子动力学特性丰富,抗噪性能优越,能够实现更低的信噪比检测,新相态判别法不受过渡过程的影响,适用于任何混沌振子且具备电路实现的可行性,配合超高频传感器可以检测超高频毫伏级的变压器局部放电信号。     

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.     

一个三维混沌系统的控制与同步

为了研究一个三维自治混沌系统的控制与同步问题,应用自适应控制方法研究混沌系统不稳定平衡点的镇定问题,得出了该系统关于平衡点渐近稳定的一个充分条件,并利用Lyapunov函数和LaSalle不变原理对结论给予了严格的证明.设计了一个较简单的控制器,采用非线性反馈控制方法研究了此混沌系统的错位同步问题,实现了响应系统和驱动系统之间的错位同步,并在Matlab上进行实例仿真.仿真结果表明自适应控制方法的快速有效性和错位同步的可实现性.     

Hyperchaos evolved from the generalized Lorenz equation

In this letter, a new hyperchaotic system is formulated by introducing an additional state into the third‐order generalized Lorenz equation. The existence of the hyperchaos is verified with bifurcation analysis, and the bifurcation routes from periodic, quasi‐periodic, chaotic and hyperchaotic evolutions are observed. Various attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit. Copyright © 2005 John Wiley & Sons, Ltd.     

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.