Implementation of a novel two-attractor grid multi-scroll chaotic system

This paper proposed a method of generating two attractors in a novel grid multi-scroll chaotic system.Based on a newly generated three-dimensional system,a two-attractor grid multi-scroll attractor system can be generated by adding two triangular waves and a sign function.Some basic dynamical properties,such as equilibrium points,bifurcations,and phase diagrams,were studied.Furthermore,the system was experimentally confirmed by an electronic circuit.The circuit simulation results and numerical simulation results verified the feasibility of this method.     

A new Rosslor hyperchaotic system and its realization with systematic circuit parameter design

Based on two modified Rosslor hyperchaotic systems, which are derived from the chaotic Rosslor system by introducing a state feedback controller, this paper proposes a new switched Rosslor hyperchaotic system. The switched system contains two different hyperchaotic systems and can change its behaviour continuously from one to another via a switching function. On the other hand, it presents a systematic method for designing the circuit of realizing the proposed hyperchaotic system. In this design, circuit state equations are written in normalized dimensionless form by rescaling the time variable. Furthermore, an analogous circuit is designed by using the proposed method and built for verifying the new hyperchaos and the design method. Experimental results show a good agreement between numerical simulations and experimental results.     

A new multi-scroll chaotic system

This paper proposes a new simple autonomous chaotic system which can generate multi-scroll chaotic attractors. The characteristic of this new multi-scroll chaotic system is that the 4n ＋ 2rn ＋ 4-scroll chaotic attractors are generated easily with n and m vaxying under n ≤ m. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on EWB （Electronics Workbench）.     

Adaptive generalized synchronization between Chen system and a multi-scroll chaotic system

Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is designed, by which the controlled Chen system can be synchronized with a multi-scroll chaotic system including unknown parameters. The Lyapunov direct method is exploited to prove that the synchronization error and parameter identification error both converge to zero. Numerical simulation results verify the feasibility of the proposed method further.     

Analysis and implementation of new fractional-order multi-scroll hidden attractors

To improve the complexity of chaotic signals,in this paper we first put forward a new three-dimensional quadratic fractional-order multi-scroll hidden chaotic system,then we use the Adomian decomposition algorithm to solve the proposed fractional-order chaotic system and obtain the chaotic phase diagrams of different orders,as well as the Lyaponov exponent spectrum,bifurcation diagram,and SE complexity of the 0.99-order system.In the process of analyzing the system,we find that the system possesses the dynamic behaviors of hidden attractors and hidden bifurcations.Next,we also propose a method of using the Lyapunov exponents to describe the basins of attraction of the chaotic system in the matlab environment for the first time,and obtain the basins of attraction under different order conditions.Finally,we construct an analog circuit system of the fractional-order chaotic system by using an equivalent circuit module of the fractional-order integral operators,thus realizing the 0.9-order multi-scroll hidden chaotic attractors.     

Comparison of performance between bipolar and unipolar double-frequency sinusoidal pulse width modulation in a digitally controlled H-bridge inverter system

By deriving the discrete-time models of a digitally controlled H-bridge inverter system modulated by bipolar sinu- soidal pulse width modulation （BSPWM） and unipolar double-frequency sinusoidal pulse width modulation （UDFSPWM） respectively, the performances of the two modulation strategies are analyzed in detail. The circuit parameters, used in this paper, are fixed. When the systems, modulated by BSPWM and UDFSPWM, have the same switching frequency, the stabil- ity boundaries of the two systems are the same. However, when the equivalent switching frequencies of the two systems are the same, the BSPWM modulated system is more stable than the UDFSPWM modulated system. In addition, a convenient method of establishing the discrete-time model of piecewise smooth system is presented. Finally, the analytical results are confirmed by circuit simulations and experimental measurements.     

Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation

The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper.A new electronic circuit unit to realize fractional-order operator is proposed.According to the circuit unit,an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system.Furthermore,synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method.Circuit experiment simulation results verify the effectiveness of the proposed scheme.     

Design and implementation of a novel multi-scroll chaotic system

This paper proposes a novel approach for generating a multi-scroll chaotic system.Together with the theoretical design and numerical simulations,three different types of attractor are available,governed by constructing triangular wave,sawtooth wave and hysteresis sequence.The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations,nonlinear functions and maximum Lyapunov exponents.In addition,the basic dynamical behaviours,including equilibrium points,eigenvalues,eigenvectors,eigenplanes,bifurcation diagrams and Lyapunov exponents,are further investigated.The success of the design is illustrated by both numerical simulations and circuit experiments.     

Multiplexing Chaotic Signals Generated by Colpitts Oscillator and Chua Circuit Using Dual Synchronization

We demonstrate multiplexing chaotic signals generated by two totally different dynamic systems (one is a Colpitts oscillator and the other is a Chua circuit) using dual synchronization and propose a method to select the proper coupling parameters. In the response systems, the cross coupling method is used, in which the voltage difference between the sum of two master oscillators and one slave oscillator is converted to current and then feed into the other slave oscillator. The result in this letter offers a potential multiuser coherent chaotic communication scheme where different chaotic oscillators can be used in one system.     

Bidirectional highly-efficient quantum routing in a T-bulge-shaped waveguide

Quantum routing in a T-bulge-shaped waveguide system coupled with a driven cyclic three-level atom and a twolevel atom is investigated theoretically.By employing the discrete-coordinate scattering method,exact expressions of the transport coefficients along three ports of the waveguide channels are derived.Our results show that bidirectional high transfer-rate single-photon routing between two channels can be effectively implemented,with the help of the effective potential generated by two atoms and the external driving.Moreover,multiple band zero-transmission emerges in the scattering spectra,arising from the quantum interferences among photons scattered by the boundary and the bulged resonators.The proposed system may suggest an efficient duplex router with filtering functions.     

基于电流反馈放大器的网格多涡卷混沌电路设计与实现

提出了一种仅用电流反馈放大器实现网格多涡卷混沌系统的方法.首先用电流反馈放大器设计非线性函数电路;再用电流反馈放大器设计网格多涡卷混沌电路,根据混沌吸引子参数确定电路参数,由于电流反馈放大器具有较好的频率特性和端口特性,使该电路的工作频率高、电路结构简单、使用元件少;最后,通过电路仿真验证该方法的可行性.     

基于同相第二代电流传输器的网格多涡卷混沌电路研究

通过简化广义Jerk系统,构建了一个三维网格多涡卷混沌系统,利用同相第二代电流传输器(CCII+)设计并实现了该系统的模拟电路,将该电路与传统运放实现的混沌电路进行了对比,发现基于CCII+的混沌电路能在更高频段产生网格多涡卷吸引子,且电路结构更简单,使用器件更少,最后,通过示波器观测到了网格多涡卷混沌吸引子,验证了混沌电路的物理可实现性,电路实验结果与数值仿真结果一致。     

用时滞和阶跃序列组合生成网格多涡卷蔡氏混沌吸引子

提出了在规范型蔡氏电路中生成两种不同类型网格多涡卷混沌吸引子的新方法.与现有文献报道仅构造同一类型非线性函数产生多涡卷混沌吸引子的主要差别在于，这种方法能在一个蔡氏电路中同时构造时滞序列和阶跃序列，并通过其不同的组合方式来扩展相空间中指标2的鞍焦平衡点，从而生成两种不同类型的网格多涡卷混沌吸引子.理论分析、数值模拟和电路实验结果证实了该方法的可行性. 关键词： 规范型蔡氏电路 网格多涡卷混沌吸引子 时滞序列和阶跃序列 电路实现     

用多项式和阶跃函数构造网格多涡卷混沌吸引子及其电路实现

提出一种利用多项式和阶跃函数构造N×M涡卷的构造方法.利用蔡氏电路,传统的利用多项式函数只能产生双涡卷、三涡卷,在此基础上,通过多项式平移得到相空间x方向的多涡卷,再通过多项式与阶跃函数组合来扩展相空间中指标2的鞍焦平衡点,使得多涡卷向y方向延伸,从而生成网格多涡卷混沌吸引子.该构造方法的主要特征是通过光滑曲线和非光滑曲线的组合生成网格多涡卷混沌吸引子,能通过调整自然数N和M的值实现平面网格任意涡卷混沌吸引子阵列.理论分析、数值模拟和电路仿真证实了方法的可行性. 关键词： 网格多涡卷混沌吸引子 蔡氏电路 阶跃函数 电路实现     

Generation and circuit implementation of multi-block multidirectional grid multi-scroll chaotic attractors

Due to the dynamic characteristics of the Chua's system, multi-scroll chaotic attractors are still confined in a single block and fail to break the limit. This paper proposes an approach for generating novel multi-block multidirectional grid multi-scroll chaotic attractors that can break the limit via novel nonlinear modulating functions. According to this method, the recursion rules used to generate multi-block multidirectional grid multi-scroll attractors are mathematically obtained. The new system is autonomous; the effectiveness of this method has been verified by theoretical analysis, numerical simulation, and circuit implementation.     

基于Colpitts振荡器模型生成的多涡卷超混沌吸引子

基于三阶单涡卷混沌Colpitts振荡器模型,通过引入两个分段线性三角波函数,构造了一个新型四维多涡卷超混沌系统,生成了(2M+1)×(2N+1),(2M+1)和(2N+1)涡卷混沌和超混沌吸引子.利用相轨图、Poincar啨映射、Lyapunov指数谱和分岔图等方法,对新提出的四维多涡卷超混沌系统进行了动力学分析,结果表明,多涡卷超混沌系统的Hopf分岔点仅与控制参数有关,而涡卷数量和控制参数的混沌和超混沌范围随着转折点数量的增加而增加.此外,设计了一个实现四维多涡卷超混沌系统的模拟电路,实验输出与数值仿真的两个结果基本一致.     

四维系统中多涡卷混沌与超混沌吸引子的仿真研究

在双涡卷混沌吸引子的基础上，以变型蔡氏电路和四阶蔡氏电路为例，提出一种研究四维系统中多涡卷混沌与超混沌吸引子的新方法.根据这一方法，从数学上找到了一种能产生多涡卷的递推规律，其特点是只需给定三个初始值ma,mb和x1，由文中所导出的递推公式，可确定多涡卷吸引子中分段线性奇函数的各个转折点和平衡点的值，从而能在四维系统中产生多涡卷混沌与超混沌吸引子，并且这种方法可以推广到产生任意多个涡卷的情形，因此，它具有一般的规律性.理论分析、计算机模拟和电路仿真结果证明了该方法的可行性.     

Generation of grid multi-scroll chaotic attractors via switching piecewise linear controller

In this Letter, a novel method is developed for generating grid multi-scroll chaotic attractors using switching piecewise linear controller. First, a third-order linear system is designed to ensure that its unique equilibrium point belongs to a saddle-focus type with index 2 and the corresponding eigenvalues satisfy Shilnikov conditions. Then, by three different types of switching control strategies, the equilibrium point can be extended along both xy plane and z axis direction, so as to generate grid multi-scroll chaotic attractors. The dynamical behaviors are further analyzed. Moreover, an improved module-based circuit is designed for realizing 5×3 and 4×4 grid scroll chaotic attractors, and the experimental results are also obtained, which is consistent with the numerical simulations.