N-涡卷超混沌吸引子产生与同步的研究

四阶MCK电路的主要特点是产生双涡卷超混沌吸引子.本文提出在该电路中产生N-涡卷超混沌吸引子的一种新方法.构造一个具有2N-1个分段线性的奇函数,其构造方法是使该函数中的每一个平衡点分别位于相邻两个转折点的正中间,并保持混沌吸引子中涡卷与键带的相互间置,在此基础上利用递推的方法求得该函数中的各个递推参数,从而可在MCK电路中产生N-涡卷超混沌吸引子.基于李雅普诺夫稳定性理论,研究了两个N-涡卷超混沌吸引子的单向耦合同步问题.最后给出了N-涡卷超混沌吸引子产生及其同步的计算机数值模拟结果.     

新型多翼统一混沌系统

通过引入多个线性状态反馈控制项和非线性状态反馈控制项,提出了一个新型多翼统一混沌系统。在不同的系统参数下均能产生关于原点对称的真实四翼混沌吸引子,还能产生蝴蝶吸引子、蝙蝠形吸引子和新型多翼混沌吸引子。采用常规的动力学分析方法研究了产生新型多翼混沌吸引子系统的基本动力学特性,例如相图、耗散性分析、李雅普诺夫指数谱和分岔图。结果表明系统可以产生丰富的混沌行为,该新型多翼混沌吸引子可以随参数的变化实现关于x轴对称的双翼混沌吸引子和关于原点对称的真实四翼混沌吸引子。     

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。     

四维系统中多涡卷混沌吸引子及其同步的研究

通过四维系统中的多涡卷混沌吸引子的研究，提出了一个简便数学公式来确定产生多涡卷的分段线性伏安特性的转折点电压，该方法可产生任意个数的涡卷。介绍了以此方法确定了产生6-8涡卷的混沌振荡电路，并对6-8涡卷的混沌振荡电路进行了仿真。最后用脉冲同步法对5涡卷混沌振荡电路进行了同步仿真研究。     

多涡卷Jerk混沌吸引子的EWB仿真

混沌吸引子的产生是将混沌信号应用于加密领域的基础。文中在双涡卷Jerk混沌吸引子的基础上,利用阶梯波函数构造产生出多涡卷Jerk混沌吸引子,分析了多涡卷Jerk混沌吸引子的产生机理,并根据无量纲状态方程,分别设计了6-涡卷和7-涡卷混沌吸引子仿真电路。利用EWB电路仿真软件进行了仿真验证,仿真结果与数学分析结果一致,证明了多涡卷Jerk系统的存在。     

一个新的混沌模型及其硬件实现

该文提出了一个新的非线性动力学系统模型并对其进行了仿真研究,结果表明此模型具有正的李雅普诺夫指数,表现出时域伪随机性和连续的频谱,因而此模型是一个混沌发生器。由于它的线性子系统的条件李雅普诺夫指数均为负,因而是可同步子系统,能够用于混沌保密通信。该文还给出了此模型的两种分段线性电路实现方法。     

一种蔡氏硬件电路系统的研究

由于混沌是貌似随机的非随机运动。它对初始条件的极端敏感性。蔡氏电路出现后,通过非线性电路研究混沌产生涡卷成为可能,而蔡氏混沌电路产生涡卷吸引子方法多种多样,利用非线性多项式产生三涡卷混沌吸引子为例,对蔡氏电路进行数学模型分析,然后进行MATLAB仿真。再此基础上,对蔡氏电路进行Multisim仿真同样可以产生三涡卷混沌吸引子,并通过硬件电路系统实现,该硬件电路能够产生三涡卷吸引子,并且可作为一个信号发生电路应用。     

多涡卷及超混沌吸引子的实验研究

简要介绍了一种用运算放大器设计多涡卷混沌振荡器的方法,该方法可产生任意个数的涡卷,并以该方法设计了一个6-8多涡卷混沌振荡器。以5涡卷混沌振荡器为例通过实验验证了其可行性,同时对双向耦合四维5涡卷混沌电路的超混沌吸引子进行了实验研究。     

三维增广Lü系统的实验验证

笔者采用模拟电路设计了一个硬件实验电路,验证了三维混沌增广Lü系统可产生复杂的混沌信号.通过一组拨位开关的转换,改变系统代数方程组表达式中常数控制项的数值,可以观察到混沌增广Lü系统既能产生两个共存的双涡卷混沌上吸引子和下吸引子,也可以实现单双涡卷混沌吸引子的转换、上下混沌吸引子的连接以及上下混沌吸引子的转换.     

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,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。     

Design and implementation of n-scroll chaotic attractors from a general jerk circuit

This paper proposes a novel nonlinear modulating function approach for generating n-scroll chaotic attractors based on a general jerk circuit. The systematic nonlinear modulating function methodology developed here can arbitrarily design the swings, widths, slopes, breakpoints, equilibrium points, shapes, and even the general phase portraits of the n-scroll chaotic attractors by using the adjustable sawtooth wave, triangular wave, and transconductor wave functions. The dynamic mechanism and chaos generation condition of the general jerk circuit are further investigated by analyzing the system stability. A simple block circuit diagram, including integrator, sawtooth wave and triangular wave generators, buffer, switch linkages, and voltage-current conversion resistors, is designed for the hardware implementations of various 3-12-scroll chaotic attractors via switchings of the switch linkages. This is the first time to experimentally verify a 12-scroll chaotic attractor generated by an analog circuit. In particular, the recursive formulas of system parameters and real physical circuit parameters are rigorously derived for the hardware implementations of the n-scroll chaotic attractors. Moreover, the adjustability of the nonlinear modulating function and the rigorous recursive formulas together provide a theoretical principle for the hardware implementations of various chaotic attractors with a large number of scrolls.     

Multi-scroll hyperchaotic system based on colpitts model and its circuit implementation

Based on the framework of Colpitts oscillator, a four-dimensional multi-scroll hyperchaotic system is proposed, which generates (2M+1)×(2N+1)-scroll chaotic and hyperchaotic attractors. The key strategy is to increase the number of index-2 equilibrium points by introducing two unit saw-tooth functions to extend and modify the Colpitts oscillator model. By using bifurcation diagram and phase portrait, the dynamical characteristics of the multi-scroll hyperchaotic system are briefly studied. Moreover, micro-controller based circuit realization is introduced and the experimental results demonstrate that 7×5-scroll chaotic and hyperchaotic attractors can be obtained in the digital circuit.     

Three-Dimensional Chaotic Autonomous System with a Circular Equilibrium: Analysis,Circuit Implementation and Its Fractional-Order Form

A three-dimensional autonomous chaotic system with a circular equilibrium is investigated in this paper. Some dynamical properties and behaviors of this system are described in terms of equilibria, eigenvalue structures, bifurcation diagrams, Lyapunov exponents, time series and phase portraits. For specific parameters, the system displays periodic and chaotic attractors. The physical existence of the chaotic behavior found in the proposed system is verified by using the Orcad-PSpice software and experimental verification. A good qualitative agreement is shown between the experimental results, PSpice and numerical simulations. Furthermore, the commensurate fractional-order version of the system with a circular equilibrium is numerically studied. It is found that chaos exists in this system with order less than three. By tuning the commensurate fractional order, the system with a circular equilibrium displays chaotic and periodic attractors, respectively. Finally, chaos synchronization of identical fractional-order chaotic systems with a circular equilibrium is achieved by using the unidirectional linear error feedback coupling. It is shown that the fractional-order chaotic system can achieve synchronization for appropriate coupling strength.     

N-涡卷超混沌吸引子的同步

首先采用Lyapunov稳定性理论证明了可以用三变量反馈实现两个N-涡卷超混沌系统的同步;然后将反馈控制与小波变换相结合,即此时发端系统的发送信号不是直接被发送,而是进行小波变换去掉细节信息,重构后再发送到收端,收端将该接收信号作为反馈信号,也可以使两个N-涡卷超混沌系统达到同步。仿真实验证明了上述结论并进一步表明,对部分吸引子,用一个信号经小波滤波后的结果作为反馈变量就能实现同步。在相关文献的基础上,减少了反馈变量数,节约了信道资源;同时,传送信号由于高频成分被滤出而成为非完整的混沌信号,不仅进一步节约了信道资源,系统的保密性也得到提高。     

Theoretical Design and Circuit Implementation of Multidirectional Multi-Torus Chaotic Attractors

This paper introduces a novel fourth-order double-torus chaotic circuit. Based on this basic circuit, a systematic theoretical design approach is proposed for generating 1-Dn torus, 2-D n times m-torus, 3-D n times m times I torus, and 4-D n times m times l times p torus chaotic attractors. This is the first autonomous circuit reported in the literature for generating multidirectional multi-torus (MDMT) chaotic attractors. The dynamical behaviors of these MDMT chaotic systems are further investigated, including equilibrium points, bifurcations, Lyapunov exponents, and Poincare maps. Theoretical analysis shows that the MDMT chaotic attractors can be generated by switching and displacing a basic linear circuit. Finally, a block circuit diagram is designed for hardware implementation of the MDMT chaotic attractors. This is also the first time in the literature to experimentally verify a maximal 1-D 20-torus, a maximal 2-D 5 times 5 torus, and a maximal 4-D 5 times 5 times 3 times 3 torus chaotic attractors.     

Generating Multi-Scroll Chaotic Attractors via?Switched Fractional Systems

A method is presented to generate multi-scroll chaotic attractors by switched fractional systems. Two sub-models in this structure are constructed by different piecewise-linear functions. It is proved that the switched systems can demonstrate multi-scroll chaotic attractors with suitable parameters and switching rule. Moreover, in order to obtain the multi-scroll chaotic attractors with the lowest system order, the relationship between Lyapunov exponents and parameters is studied. It is found that the multi-scroll chaotic attractors can be presented with a system order larger than 0.9. Numerical examples are provided to illustrate the effectiveness of the proposed scheme.     

一种四螺旋混沌系统仿真研究

为了改善Lü系统的混沌特性,通过在混沌Lü系统上添加一维线性状态反馈控制器,构建了一个新的四维连续自治混沌系统,得到了奇异的四螺旋鲁棒混沌吸引子。利用相轨图、Lyapunov指数谱等数值方法,其最大Lyapunov指数为正值且几乎恒定不变,系统具有很好的鲁棒性.随控制参数变化,系统能够从四螺旋混沌吸引子演变成双螺旋混沌吸引子。通过在混沌Lü系统电路上外加一个简单的线性积分电路实现了新混沌系统的实验电路,实验仿真与数值方法所得结果有着很好的一致性。