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 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.     

Multi‐scroll chaotic attractors from a generalized time‐delay sampled‐data system

In this paper, the first generalization for time‐delay sampled‐data chaotic system in order to generate multi‐scroll attractor is introduced with its circuit implementation. An efficient delay‐line with binary priority encoding, parallel shifting, and binary decoding is also suggested and implemented to overcome the delay line realization drawback in such systems. The proposed system enhances the complexity of chaotic behavior by means of multi‐scroll feature and exemplifies the simplification of chaotic systems for better realizations. Copyright © 2015 John Wiley & Sons, Ltd.     

On constructing complex grid multi‐wing hyperchaotic system: Theoretical design and circuit implementation

This paper further investigates some novel methods for generating complex grid multi‐wing hyperchaotic attractors from four‐dimensional (4D) quadratic hyperchaotic systems, based on our previous works. First, a modified double‐wing hyperchaotic Lü system by using non‐uniform variable scaling transformation is obtained, and n‐wing hyperchaotic system equipped with a duality‐symmetric multi‐segment quadratic function is also constructed. Then, by switching control in the z direction, mirror symmetry conversion and rotation transformation, three classes of n × m‐wing hyperchaotic systems are respectively realized. Finally, two types of improved module‐based circuits are designed for generating various grid multi‐wing hyperchaotic attractors. One characteristic of the proposed approaches lies in their generality, which is also suitable for constructing 4D grid multi‐wing hyperchaotic Lorenz and Chen systems. Both numerical simulation and circuit implementation have demonstrated the feasibility and effectiveness of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive actuator failure compensation design for unknown chaotic multi‐input systems

In this paper, an adaptive control approach is designed for compensating the faults in the actuators of chaotic systems and maintaining the acceptable system stability. We propose a state‐feedback model reference adaptive control scheme for unknown chaotic multi‐input systems. Only the dimensions of the chaotic systems are required to be known. Based on Lyapunov stability theory, new adaptive control laws are synthesized to accommodate actuator failures and system nonlinearities. An illustrative example is studied. The simulation results show the effectiveness of the design method. Copyright © 2014 John Wiley & Sons, Ltd.     

Circuit implementation and model of a new multi‐scroll chaotic system

In this paper, a multi‐scroll chaotic system from the improved Chua's system is proposed. Moreover, non‐linear dynamics are analyzed including phase‐space trajectories, bifurcation diagrams, Poincaré maps and so on. The most important thing is that we discovered phase‐space trajectories, bifurcation diagrams and Poincaré maps are unified and closely related, which can describe different aspects of the multi‐scroll chaotic system. Furthermore, the corresponding improved module‐based circuits are designed for realizing two to four‐scroll chaotic attractors, and the experimental results are also obtained, which are consistent with the numerical simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

混沌时间序列预测在短期电力负荷预测中的应用

混沌吸引子具有空间的遍历性、总体的稳定性、吸引性和内部分形性，使得混沌预测成为可能。采用非线性系统理论对电力系统的历史数据进行分析，并基于改进的混沌吸引子模型对山西电网实际负荷数据进行短期预测，预测结果相对误差小、精度高，为电力系统短期负荷预测提供了一种新的预测方法。     

混沌时间序列预测在短期电力负荷预测中的应用

混沌吸引子具有空间的遍历性、总体的稳定性、吸引性和内部分形性,使得混沌预测成为可能。采用非线性系统理论对电力系统的历史数据进行分析,并基于改进的混沌吸引子模型对山西电网实际负荷数据进行短期预测,预测结果相对误差小、精度高,为电力系统短期负荷预测提供了一种新的预测方法。     

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。     

高压断路器机械振动信号混沌吸引子形态特性

提出并探讨了基于混沌吸引子形态特性的高压断路器振动信号特征提取方法。采用功率谱和Lyapunov指数分别对高压断路器振动信号进行定性和定量混沌分析,证实了高压断路器振动信号既包含高压断路器动力学特性,也存在混沌现象;在此基础上,对振动信号进行相空间重构,分析混沌吸引子形态特性与故障类型之间的关系;最后,以不同严重程度的分闸缓冲器故障为例,深入探讨了不同严重程度故障下混沌吸引子的演变规律。研究结果表明,高压断路器振动信号混沌吸引子形态在同一故障状态下较稳定,对故障类型及故障严重程度较敏感,这表明混沌吸引子形态特性是研究高压断路器振动信号特征提取的有效实用途径。     

电压模式控制Buck变换器中的混沌吸引子重构技术

利用Buck变换器的输出电压时间序列可以进行变换器的混沌吸引子重构，其中延迟量可以通过时间序列的自相关函数来确定，而重构维数也可根据混沌吸引子的关联维来确定，仿真和特征参数计算均表明Buck变换器的重构混沌吸引子与原混沌吸引子拓扑等价，具有相同的动力学性质和几何性质，另外，构建了一个延迟重构实验电路，得到的实验波形也验证了上述结果。     

电压模式控制Buck变换器中的混沌吸引子重构技术

利用Buck变换器的输出电压时间序列可以进行变换器的混沌吸引子重构，其中延迟量可以通过时间序列的自相关函数来确定，而重构维数也可根据混沌吸引子的关联维来确定，仿真和特征参数计算均表明Buck变换器的重构混沌吸引子与原混沌吸引子拓扑等价，具有相同的动力学性质和几何性质，另外，构建了一个延迟重构实验电路，得到的实验波形也验证了上述结果。     

基于遗传算法的混沌系统多模型微扰控制

针对基于遗传算法的混沌系统多模型控制问题,为扩大控制器在吸引子中的作用范围,采用遗传算法引导混沌轨道的方法产生多模型控制策略,能使混沌系统在小的扰动作用下迅速从某一初始点到达目标点。对含有不确定参数的Henon混沌系统仿真表明,与其他方法相比能在更短的暂态时间内把系统控制到预定轨道。     

Generation of n-double scrolls via cellular neural networks

N-double scrolls are chaotic attractors generated by Chua's circuit when its non-linear resistor characteristic is appropriately modified. They have recently been introduced, simulated and studied analytically by Suykens and Vandewalle. In this paper a new approach to generate n-double scroll attractors is introduced. They have been derived from a connection of three simple generalized cellular neural network cells called a state controlled CNN (SC-CNN). In this way it is established that n-double scroll attractors can be generated using an SC-CNN. The circuit implementation of the introduced system and some experimental results referring to the 2-double scroll attractor are reported.     

一类非线性混沌系统的RBF神经网络控制

设计了一种基于径向基函数网络(RBFNs)的混沌非线性动力系统控制方法，将嵌入在混沌吸引子中不稳定周期轨道镇定到稳定不动点。用Logistic方程和Henon映射作数值仿真实验，证明了该方法的有效性。     

基于虚拟仪器四翼混沌吸引子的研究

随着虚拟仪器技术的飞速发展,为研究非线性系统提供了新途径。讨论了基于虚拟仪器四翼混沌吸引子的研究模式,设计了软件系统,并给出了基于虚拟仪器技术实验系统的拓扑结构,为研究非线性系统提供了可行的方案。利用此方案进行初步的实验,结果证明此实验系统在参数调节方面、可靠性,实时性等具有良好的实验效果。     

基于超混沌的电力线直序扩频序列

提出一种新的超混沌系统,通过分析该系统的动力学特性,可知该系统的混沌吸引子不同于已发现的混沌吸引子,且该系统具有较高的李亚普诺夫指数,是一种新的超混沌系统。利用该系统产生的混沌序列生成扩频序列,理论分析表明,该扩频序列具有良好的平衡性、相关性及保密性能。将该扩频序列引入电力线直序扩频系统中,仿真结果表明所产生的扩频序列具有良好的抗多用户干扰的性能,且提高了系统的保密性能,适合于电力线直序扩频通信系统中。     

Creation and circuit implementation of two-to-eight–wing chaotic attractors using a 3D memristor-based system

This paper constructs a three-dimensional (3D) memristor-based system for creating multiwing chaotic attractors. A second-degree polynomial memristance function and a sixth-order exponent internal state memristor function with one parameter are employed, and the complexity of attractors is increased. A detailed analysis on dynamical behaviors of the proposed system are described, such as the bifurcation diagrams, finite-time local Lyapunov exponents, time series, phase portraits, and Poincaré maps. By adjusting the design parameters, the system displays two-to-eight–wing chaotic attractors, especially the five-wing and seven-wing attractors, which have never been found in the known systems. Further, we provide the calculation formula of the number of wings in the system, discuss the distribution of the involving inner holes on the plane, and design an electronic circuit to realize the proposed system. The experimental results of the circuit implementation agree with the numerical simulations on Matlab well. It indicates the potential engineering applications for various chaos-based information systems.     

电力短期负荷时间序列混沌特性分析的技术改进

电力短期负荷具有混沌特性。通过深入研究其混沌吸引子的形状、关联维数及最大Lyapunov指数,发现这些混沌特征数对电力短期负荷预测具有重要意义。在相空间重构的基础上,经研究发现电力短期负荷二维相图两坐标间延迟时间为8时,其混沌吸引子能得到最好的再现;对计算关联维数的G-P算法中关键参数的选取提出了简单易行的方法,使该算法更易于操作;对计算最大Lyapunov指数的小数据量方法做进一步改进,提出了一套固定参数,并用Henon系统数据验证了该方法的有效性。用上述改进方法进一步分析了电力短期负荷的混沌特性。     

A combined approach for the identification of continuous non‐linear systems

The identification of a non‐linear continuous output‐only system from a time series is considered for the case that the functional form of the model is not known beforehand. To estimate both functions and parameters, a combination of non‐parametric modelling based on non‐linear regression and parametric modelling based on a multiple shooting algorithm is proposed. This strategy to determine non‐linear differential equations is exemplified on experimental data from a chaotic circuit where an accurate reconstruction of the observed attractor is obtained. Copyright © 2003 John Wiley & Sons, Ltd.