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.     

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.     

超磁致伸缩作动器的分岔和混沌行为

混沌和拟周期运动是两种不稳定的响应，为研究超磁致伸缩作动器的这些不稳定行为，建立了其非线性动态力学模型，用数值方法得到了反映系统非线性响应特性的分岔图、相图、Poincaré截面图、幅值谱等。分析结果表明：阻尼系数的增加，有助于系统输出的稳定；系统刚度过低，会导致混沌现象的出现；激励电流的角频率对系统的响应特性有很大的影响。     

Classical and quantum mechanical transport simulations in open quantum dots

Simulations of open dot arrays are performed where the electron motion is considered in a harmonic potential and in a static magnetic field. Results concern electron trajectories and Poincaré sections from the classical calculation. The analysis of the Poincaré sections reveals a strong influence of the length of the constriction on the chaotic regions in phase space. Density probabilities from the quantum mechanical calculation show a significant correspondence to classically calculated trajectories.     

Novel chaotic behavior in the Muthuswamy–Chua system using Chebyshev Polynomials

In this paper, three kinds of memristors with memristance functions obtained from the Chebyshev polynomials are used in the Muthuswamy–Chua system, which has only three circuit elements: a linear passive inductor, a linear passive capacitor and a nonlinear active memristor. We use multivariable second‐order polynomial functions of current and memristor state for the internal state function of the memristor. This enables our system to generate not only double‐scroll but also four‐scroll attractors. Systematic studies of chaotic behavior in these systems are performed using phase portraits, bifurcation diagrams and Lyapunov exponents. Simulation results show that all these systems exhibit chaotic behavior over a range of control parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

基于分岔理论的铁磁谐振研究

电力系统的铁磁谐振所产生的过电压严重威胁系统的安全稳定运行。为了了解系统响应性质随系统参数变化的情况,基于分岔理论,对一典型的110 kV变电站系统进行了数值仿真研究,绘制了以电源电压为分岔参数的分岔图,并结合系统的时域、频域、相图和庞加莱映射,分析了该系统所表现的基频、分频和混沌谐振。研究结果表明,分岔图能够很好的显示系统在某一参数范围内的全局性质,有利于为提出抑制谐振措施拓宽思路。     

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.     

Qualitative analysis of an interrupted electric circuit with spike noise

Switching non‐ideality and its effects have been reported in DC‐DC converters. In this paper, we examine the qualitative property of an interrupted electric circuit with spike noise. First, we show the circuit model that have the switch interrupted by its own state and a periodic interval. Here, we artificially add spike noise via every switching action. Then, we explain its dynamics and derive the Poincaré map for the rigorous analysis in a circuit with ideal switching and a circuit with spike noise, respectively. Finally, we discuss the dynamical effects of spike noise from experimental and analytical viewpoints based on the Poincaré map and bifurcation diagrams. As a result, some dynamical effects of spike noise are clarified in terms of the invariant set, bifurcations, and existence regions of coexisting attractor. Copyright © 2010 John Wiley & Sons, Ltd.     

A multi‐wing butterfly chaotic system and its implementation

It has been a common brief that the principle for generating multi‐wing attractor from a Lorenz‐like chaotic system is to construct an even symmetric function for the system. In this pursuit, research effort on exploring the possibility of using non‐even symmetric function is scant, if any. This paper attempts to reveal the intrinsic relation between such a system function and its generated multi‐wing attractor in a chaotic system. It will be shown that a rather simple asymmetric function applying to the Shimizu–Morioka system can indeed generate a multi‐wing butterfly chaotic attractor. Then, some basic properties, compound structure, bifurcation diagram, Lyapunov exponent spectrum, and dynamical analysis of the new chaotic system are investigated in detail. Finally, an electronic circuit is designed and its experimental results are presented, which well match the numerical simulation results, thereby verifying the feasibility of the new method. Copyright © 2017 John Wiley & Sons, Ltd.     

Spiral periodic structure inside chaotic region in parameter‐space of a Chua circuit

In this letter we investigate, via numerical simulations, the parameter‐space of the set of autonomous first‐order differential equations of a Chua circuit. We show that this parameter‐space presents self‐organized periodic structures immersed in a chaotic region, forming a single spiral structure that coils up around a focal point. Additionally, bifurcation diagrams are used to show that those periodic structures also organize themselves in period‐adding cascades, along specific directions that point towards this same focal point. Copyright © 2010 John Wiley & Sons, Ltd.