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。     

三维多涡卷Colpitts混沌系统及其数字硬件实现

基于混沌吸引子形成的机理,利用单位锯齿波函数改造混沌Coipitts振荡器模型,提出了一个新三维多涡卷混沌系统,生成了(2K+1)涡卷混沌吸引子.单位锯齿波函数的引入,增加了系统的指数2平衡点,从而形成多涡卷吸引子.采用常规的动力学分析方法,研究了该多涡卷混沌系统的动力学特性,研究结果表明所提出的系统的Hopf分岔点仅...     

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。     

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。     

多涡卷超混沌电路及其耦合同步的仿真与实验研究

为了产生更复杂的混沌系统，本文利用两个(或更多)多涡卷混沌电路的耦合构成了多涡卷超混沌系统，两个这样的超混沌系统可以通过耦合达到同步。仿真和实验结果使此类超混沌系统及其同步得到了验证。     

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.     

基于考毕兹振荡器的宽带混沌电路设计

针对某些雷达、通信等系统在应用中对混沌信号频域带宽的要求,设计了一种基于考毕兹振荡器电路的宽带混沌信号发生器。该混沌信号产生电路由考毕兹振荡器为基本谐振电路、级联若干容阻串并联单元的选频网络构成,混沌信号的上下限频率分别由基本谐振电路和第一节容阻串并联网络参数决定,通带频谱的平坦性受其他级联选频网络影响。根据初步分析和仿真试验,该混沌电路组成结构简单,能够产生带宽超过60MHz较为平坦的宽带混沌信号。     

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。     

A new multi-scroll Chua’s circuit with composite hyperbolic tangent-cubic nonlinearity: Complex dynamics,Hardware implementation and Image encryption application

In this paper, a new method for generating multi-scroll chaotic attractors via constructing a compound hyperbolic tangent-cubic nonlinear function in canonical Chua’s circuit is presented. The basic dynamic characteristics of the system are analyzed, including equilibrium points, bifurcation diagrams, Lyapunov exponents, phase portraits, time-domain diagrams and attractive basins. What is surprising is that the proposed multi-scroll Chua’s circuit also exhibits rich dynamic behaviors like coexisting multiple attractors, transient period, intermittent chaos and offset boosting. In addition, we put forward the application of the system in chaotic image encryption, and analyzed some security performance evaluation indexes to show that the new Chua’s chaotic cipher system has high security and reliable encryption performance. Finally, the hardware design and experiments of the chaotic digital circuits and image encryption are carried out. Both numerical simulation and FPGA experimental results verify the feasibility and usability of the proposed new multi-scroll Chua’s system.     

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。     

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.     

Colpitts振荡电路动力学特性的PSPICE仿真分析

以Colpitts振荡器电路为例,在建立Colpitts电路模型的基础上,对其进行PSpice仿真研究,观察状态变量分别在时域和频域中的变化.通过调整电路元件的参数,观察Colpitts电路中动力学行为的演变过程,得到了与理论分析相吻合的结果.可以发现,电路处于混沌态和准周期态的参数组合不是唯一的.     

Two-stage chaotic Colpitts oscillator

A novel version of the chaotic Colpitts oscillator is proposed. It contains two bipolar junction transistors coupled in series. The resonance loop consists of an inductor and three capacitors. The two-stage oscillator, compared with the classical circuit, enables the fundamental frequency of chaotic oscillations to be increased by a factor of three. The PSpice simulations performed with 9 GHz threshold frequency transistors demonstrate that the highest fundamental frequencies of chaotic behaviour are 1 and 3 GHz for the classical and the two-stage Colpitts oscillator, respectively     

A comparison of five methods for studying a hyperchaotic circuit

A hyperchaotic oscillator based on an LC oscillator and the Deliyannis single amplifier biquad (SAB), coupled by means of a diode, is studied. The inductor of the resonant circuit is realized in practice by using a generalized impedance converter (GIC). Various methods for detecting chaos, such as the Lyapunov exponents, the Lyapunov dimension, the Poincaré map, the spectrum and the phase portraits, are used, in order to confirm the chaotic behaviour of the chaotic circuit. Experimental results fully coincide with theoretical and simulation results. The paper also attempts to answer the question ‘which of the above methods is the most preferable, and why?'. It is concluded that the Lyapunov exponents, Lyapunov dimension and Poincaré map constitute the more reliable methods of confirming chaos.     

一类3涡卷混沌吸引子产生与同步的研究

提出利用符号函数产生3涡卷混沌吸引子的方法,进行基本的混沌动力学分析,给出最大李雅普诺夫指数、功率谱、庞加莱映射,并基于李雅普诺夫稳定性理论,研究了两个3涡卷混沌吸引子的单向耦合同步的问题,给出3涡卷混沌吸引子产生及其同步的数值模拟结果.     

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。     

Improved chaotic Colpitts oscillator for ultrahigh frequencies

A novel version of the Colpitts oscillator is presented generating chaotic oscillations at gigahertz frequencies. In contrast to the standard oscillator the inductor is moved from the collector circuit of the transistor to the base circuit. PSpice simulations demonstrate chaos at the fundamental frequencies of 0.5, 1 and 2 GHz employing transistors with a threshold frequency of 9 GHz.     

一种基于Logistic电平脉冲的多涡卷系统及其图像加密应用

现有多涡卷吸引子混沌系统中引入的非线性函数多为阶梯函数、饱和函数、多逻辑电平脉冲函数等,从而系统的电路实现复杂度会随涡卷数量的增加而增大,致使其硬件实现变得较为困难。针对此问题,该文设计了Logistic电平脉冲函数,采用非自治的脉冲控制方法基于Lorenz系统构造了一个新的多涡卷混沌系统,对其进行了动力学特性分析和基于FPGA芯片的硬件实现,最后给出了系统在图像加密中的应用。分析结果表明,该文所设计系统的电路实现复杂度与涡卷数量无关,于是FPGA电路可在不改变RTL代码的情况下仅通过改变控制参数即可产生不同的多涡卷吸引子;与Lorenz系统相比,此多涡卷系统具有更多的敏感性参数,应用于图像加密时密钥空间更大,更能有效抵抗穷举攻击。     

Electronic simulation and microcontroller real implementation of an autonomous chaotic and hyperchaotic system made of a Colpitts-Josephson junction like circuit

Most of the simple Josephson junction (JJ) based circuits with chaotic behavior found in the literature are nonautonomous. Hyperchaotic JJ-based circuits are often either driven by an external force or result from coupling chaotic circuits. An autonomous simple circuit based on Josephson junction active element (JJ), with exactly three physical energy storage tanks, is proposed and analyzed in this paper. This Colpitts-like CLC circuit, though operating at low frequencies, can generate hyperchaotic signals when its nonlinear element is a resistive–capacitive–inductance shunted junction (LRCLSJ) model. Two equilibrium points are found, and their stability analysis is investigated. The proposed circuit displays Hopf bifurcation, periodic oscillations, chaotic and hyperchaotic attractors. The electronic implementation of the proposed circuit using OrCAD-PSpice software is presented to confront the numerical simulations results. A good qualitative agreement is revealed by comparing the analog and numerical simulations results. At last, the microcontroller real implementation is presented using Arduino UNO board. The results obtained are in good agreement with the numerical simulation results.

     

The multi-scroll hyper-chaotic coexistence attractors and its application

Applying a chaotic system to digital image communication is an effective way to resist the attack of intelligent system with strong computing power. However, the traditional chaotic systems lack more complex dynamic behavior that is very valuable for a series of applications. Based on Lorenz system, this study proposes a hyper-chaotic system with multi-scroll coexistence attractors by using a piecework function. Through bifurcation diagram and Lyapunov exponents, we analyzed the dynamic behavior of the system, and observed multi-scroll coexistence attractors in the numerical simulation. The results show that compared with the traditional chaotic attractor, multi-scroll coexistence attractor has more complex structure and dynamic behavior. Furthermore, we design a cryptosystem based on this system for the digital image. Scrambling and diffusing images with the sequence of multi-scroll coexistence attractors can destroy the correlation of adjacent pixels and hide the information of all pixels. Theoretical analysis and simulation on key space, histogram, information entropy, key sensitivity and pixel correlation show that the encryption scheme is feasible and secure.