Generating one-,two-,three-and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincare maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.

Coexisting and multiple scroll attractors in a Hopfield neural network with a controlled memristor

A method of generating multi-double scroll attractors is proposed based on the memristor Hopfield neural network(HNN)under pulse control.First,the original hyperbolic-type memristor is added to the neural network mathematical model,and the influence of this memristor on the dynamic behavior of the new HNN is analyzed.The numerical results show that after adding the memristor,the abundant dynamic behaviors such as chaos coexistence,period coexistence and chaos period coexistence can be observed when the initial value of the system is changed.Then the logic pulse is added to the external memristor.It is found that the equilibrium point of the HNN can multiply and generate multi-double scroll attractors after the pulse stimulation.When the number of logical pulses is changed,the number of multi-double scroll attractors will also change,so that the pulse can control the generation of multi-double scroll attractors.Finally,the HNN circuit under pulsed stimulation was realized by circuit simulation,and the results verified the correctness of the numerical results.

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.

Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

A novel 5-dimensional（5D） memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincar′e map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.

Synchronization of two 3-scroll hyperchaotic attractors using wavelet transform

The synchronization of two 3-scroll hyperchaotie attractors is realized based on wavelet transform and single variables＇ feedstock. In the transmitter, one signal is decomposed by wavelet transform and the detailed information is removed, then the component with low frequency is reconstructed and sent into the channel In the receiver, the received signal is used as the feedback signal to realize the synchronization of two chaotic systems. Using this synchronous method, the transmitting signal is transported in compressible way, the system resource is saved, furthermore, because the transported signal is not a whole chaotic signal, the performance of security of the system is improved.

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.

A new multi-scroll chaotic generator

In this paper a new simple multi-scroll chaotic generator is studied. The characteristic of this new multi-scroll chaotic generator is that it is easy to generate different number of scroll chaotic attractors through modifying the nature number n after fixing the suitable system parameters and it does not need complex mathematical derivation. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on Electronic Workbench （EWB）.

具有多种吸引子共存类型的新型四维混沌系统

为了产生多种共存吸引子,本研究构建了一个具有多稳定性的新型四维耗散混沌系统。通过相图、Lyapunov指数谱、分岔图等的数值仿真,分析了此系统的动力学行为。设计了系统的模拟电路,并用Multism进行了仿真,亦制作了系统的现场可编程门阵列(FPGA)数字电路。模拟电路仿真结果和数字电路实现结果与数值仿真结果相符,验证了系统的混沌行为,亦表明了其可实现性。系统具有如下重要特性:在不同的参数取值下,系统存在10种吸引子共存类型,涉及的共存吸引子有点吸引子、不同的周期吸引子、拟周期吸引子、不同的混沌吸引子;系统特性对参数具有较强的灵敏性,即随着参数的变化,系统整体运行状态频繁地在周期和混沌状态之间切换;参数可以影响系统吸引子的拓扑形状,即随着参数的变化,系统吸引子的形状从单涡卷吸引子到双涡卷吸引子,最后到四涡卷吸引子。

基于反正切的网格混沌吸引子及其保密通信

提出了一种用处处光滑的反正切函数序列生成多维多涡卷网格混沌吸引子的方法,可以生成一维n涡卷、二维n×m网格多涡卷和三维n×m×l网格多涡卷混沌吸引子。平衡点分析、数值仿真、Lyapunov指数谱、分岔图和Poincaré映像都表明系统是混沌的。用简单的线性反馈控制实现了同结构网格多涡卷混沌系统之间的同步,可应用于保密通信。简单的理论分析和数值仿真证明了该方法的有效性。

多涡卷Chua混沌吸引子的设计与性能分析

为了设计结构复杂、性能优越的多涡卷混沌系统,采用理论分析和数值仿真的方法,通过设计一个连续非线性函数,建立了三阶Chua系统的单方向与网格多涡卷吸引子模型.在Matlab平台上,通过吸引子相图、最大Lyapunov指数、分岔图和Poincaré截面等方法,分析了多涡卷Chua混沌系统的动力学特性.研究结果表明,多涡卷Chua混沌吸引子具有丰富的动力学特性,仿真结果与理论分析一致,表明了多涡卷Chua混沌系统设计方法的有效性和设计模型的正确性.

耦合负反馈超混沌系统及在编码通信中的应用

证明了耦合负反馈蔡氏电路超混沌系统 ,其动力学行为产生 4对双涡旋吸引子超混沌现象 .在编码通信混沌隐藏和混沌键控技术应用方法中提出并数值模拟研究该超混沌现象 .

限幅法控制蔡氏电路及5涡卷混沌吸引子的实验研究

利用限幅控制法对基于模拟电感的双涡卷以及5涡卷混沌进行了电路实验控制研究.结果表明:利用二极管构成的双向限幅控制电路,仅通过改变限幅电压即可得到非常好的控制效果;该控制方法不受系统的频率限制,无需预先知道系统较多的动力学信息,实验装置简单,在实际系统中容易实现.

基于虚拟仪器技术新型混沌信号产生器的设计

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技术的新型混沌信号产生器的实验模式,设计了硬件系统和软件系统,并给出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具有良好的实验效果。

用FPGA技术产生多涡卷超混沌吸引子的研究

提出用FPGA技术产生多涡卷超混沌吸引子的新方法。基于数字信号处理技术,对连续混沌系统进行离散化处理和变量比例变换,使离散化后的混沌系统便于FPGA实现。文中以四阶蔡氏超混沌系统为典型实例,给出了用FPGA技术产生多涡卷超混沌吸引子的实验结果。

n×m涡卷混沌吸引子的研究及硬件实现

提出了产生n×m涡卷混沌吸引子的一种新方法,用三角波函数序列和阶跃函数序列构造网格多涡卷混沌系统,找出函数中平衡点和转折点的值,并对系统的基本动力学特性进行了研究,包括理论分析和计算机模拟仿真。用模块化的方法设计了现场可编程门阵列(FPGA)硬件实验电路,给出了相关的实验结果。计算机仿真和FPGA硬件实验结果相吻合,由此证明了该系统的混沌特性。

多涡卷超混沌系统的设计与性能分析

为了设计性能优越的多涡卷超混沌系统,采用理论分析和数值仿真方法,通过设计一个连续的非线性函数,得到了6阶超混沌系统的单方向与网格多涡卷吸引子模型。通过吸引子相图、Lyapunov指数谱、分岔图、Poincaré截面和复杂度等,分析了多涡卷超混沌系统的动力学特性。研究结果表明:多涡卷超混沌吸引子具有丰富的动力学特性,仿真结果与理论分析结果一致,表明了多涡卷超混沌系统设计方法的有效性和设计模型的正确性。

基于忆阻器的混沌电路设计与硬件实验

通过在经典QI混沌系统中加入三次非线性磁控忆阻器,构造出了一种四维忆阻混沌系统。分析了该系统的基本动力学特性,证明该系统可以产生混沌吸引子。设计了硬件电路,通过改变元件参数观察到不同类型的吸引子和极限环,实验结果与仿真结果相符合。提出的基于忆阻器的混沌电路设计与硬件实验方案不仅可以拓展传统混沌电路的实现方法,还为非线性电路设计等相关课程的实验教学提供新思路,对实践教学的发展起到一定的促进作用。

Colpitts电路中的双涡卷混沌寄生振荡分析

通过在Colpitts振荡器中引入二次反馈项,观察到了新奇的双涡卷吸引子.这个具有反馈项的混沌系统具有3个平衡点,产生不同于Lorenz和Colpitts系统的复杂吸引子.对系统的一些基本特性,如平衡点、稳定性、Lyapunov指数谱、分岔图、相轨与庞加莱截面等进行了详细的分析.

一种网格多涡卷混沌Colpitts振荡器及其电路实现

基于单涡卷混沌Colpitts振荡器模型,对使用不同非线性函数构造多涡卷混沌Copitts振荡器模型进行了研究,并提出了一种网格多涡卷混沌Colpitts振荡器模型。利用阶跃函数代替单涡卷混沌Colpitts振荡器模型中的非线性函数,以及增加一个饱和函数,构造了一个能产生网格多涡卷混沌吸引子的Colpitts振荡器模型。通过数值仿真与电路实验,验证了该网格多涡卷混沌Colpitts振荡器的可行性。

基于多涡卷混沌吸引子的电力电子变换器混沌PWM控制研究

基于多涡卷混沌吸引子,提出了一种新型混沌PWM控制方法抑制电力电子变换器电磁干扰。该方法将多涡卷混沌吸引子与传统混沌PWM控制结合,应用于电力电子变换器的控制中,实现从电磁干扰源头上抑制传导电磁干扰。对比传统混沌PWM控制,该方法能够在降低开关频率及其倍数次谐波峰值的同时,减少开关频率及其倍数次附近次谐波的生成,具有更好的EMI抑制效果。