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。     

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。     

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。     

电流型网格多涡卷混沌电路的设计与实现

以电流为状态变量,提出了一种基于电流传输器的电流模式网格多涡卷混沌电路。该电路由电流积分器、电流比例运算电路和电流模式阶梯波序列电路构成。相对于传统的电压模式混沌电路,该电流模式多涡卷混沌电路具有宽频谱、低功耗和便于集成等优点。通过改变系统的时间常数τ,对比研究了电流模式混沌电路和电压模式混沌电路的高频性能。Pspice仿真结果表明,提出的电流模式混沌电路能够产生高频率的多涡卷混沌吸引子。     

复合型混沌系统的设计与仿真

基于切换控制的方法设计了一个同时拥有多翅膀和多涡卷混沌吸引子的四维复合型混沌系统.通过观察复合型混沌系统的相图、分岔图和Lyapunov指数谱,分析了该系统动力学行为.根据Matlab数值仿真的结果,得出了该复合型混沌系统是超混沌系统,并且其最大Lyapunov指数大于复合前两个系统的最大Lyapunov指数,说明该系...     

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.     

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。     

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...     

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.     

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.     

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.     

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.     

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.     

一种具有多对称同质吸引子的四维混沌系统的超级多稳定性研究

该文在一个经典3维混沌系统的基础上提出一个新的具有超级多稳定性的4维混沌系统.新系统具有一个线平衡点,可以产生无限多对称的同质吸引子.通过相轨图和庞加莱截面等方法分析了系统的混沌特性.重点利用相轨图、分岔图和Lyapunov指数谱等方法分析了初始条件对系统超级多稳定性的影响,分析表明该系统具有很大的初值变化范围,除零点...     

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。