Sequences of gluing bifurcations in an analog electronic circuit

We report on the experimental investigation of gluing bifurcations in the analog electronic circuit which models a dynamical system of the third order: Lorenz equations with an additional quadratic nonlinearity. Variation of one of the resistances in the circuit changes the coefficient at this nonlinearity and replaces the Lorenz route to chaos by a different scenario which leads, through the sequence of homoclinic bifurcations, from periodic oscillations of the voltage to the irregular ones. Every single bifurcation “glues” in the phase space two stable periodic orbits and creates a new one, with the doubled length: a sequence of such bifurcations results in the birth of the chaotic attractor.     

一种新型的四维多翼超混沌吸引子及其在图像加密中的研究

提出了一种新的能产生多翼混沌吸引子的四维混沌系统,该系统在不同的参数条件下能产生混沌、超混沌吸引子.然后对此混沌系统的一些基本的动力学特性进行了理论分析和数值仿真,如平衡点、Poincaré映射、耗散性、功率谱、Lyapunov指数谱、分岔图等.同时设计了一个模拟振荡电路实现四翼超混沌吸引子,硬件电路模拟实验结果与数值仿真结果相一致.最后将此四维多翼超混沌系统用于物理混沌加密和高级加密标准加密级联的混合图像加密算法,这种利用物理混沌不可预测性的混合加密系统,不存在确定的明文密文映射关系,且密文统计特性也比其他加密系统要好.     

On the dynamics,existence of chaos,control and synchronization of a novel complex chaotic system

In this paper, the authors have studied the dynamics of a novel complex chaotic system with fractional order derivative and found the existence of chaos. The novel complex system is simulated for integer as well as fractional orders which shows some unusual phenomena. The main contribution of this effort is an implementation of the Largest Lyapunov Exponent (LLE) criteria based on Wolf’s algorithm. The conditions for chaos control based on the fractional Routh–Hurwitz stability conditions and feedback control are given. Also synchronization between a fractional order novel chaotic system and a controlled fractional order novel system using the modified adaptive projective synchronization method for different scaling matrices has been obtained. Numerical simulation results are carried out using the Adams–Bashforth–Moulton method.     

含有单相铁芯变压器的铁磁混沌电路的分析及控制

对一个含有单相铁芯变压器的三阶非自治铁磁混沌电路进行了理论研究和计算机仿真分析.研究表明,仅含由磁通链控制的非线性电感器件的三阶非自治电路可以作为一个四阶自治改进系统来分析.数值仿真和电路实验证实了此系统确实存在混沌动力学行为.同时,还提出了一种通过改变线性电容参数控制混沌的方法.     

基于最小二乘支持向量机的分数阶混沌系统控制

提出了基于最小二乘支持向量机(LS-SVM)的分数阶混沌系统控制方法.基于分数阶线性系统稳定理论,通过线性分离的方法将系统分解为稳定的线性部分和相应的非线性部分,再利用支持向量机良好的非线性函数逼近和泛化能力设计了主动控制器,对非线性部分进行补偿,从而将分数阶混沌系统控制到平衡点.分别以分数阶Liu系统和分数阶Chen系统为例进行了仿真研究,表明该方法是有效和可行的.     

Chaotic behavior in noninteger-order cellular neural networks

In this paper, a simple system showing chaotic behavior is introduced. It is based on the well-known concept of cellular neural networks (CNNs), which have already given good results in generating complex dynamics. The peculiarity of the CNN model consists in the fact that it replaces the traditional first-order cell with a noninteger-order one. The introduction of the fractional cell, with a suitable choice of the coupling parameters, leads to the onset of chaos in a simple two-cell system. A theoretical approach, based on the harmonic balance theory, has been used to investigate the existence of chaos. A circuit realization of the proposed fractional two-cell chaotic CNN is reported and the corresponding strange attractor is also shown.     

利用单驱动变量实现一类分数阶混沌系统的修正投影同步

通过设计一个合适的响应系统,提出了一种修正投影同步方案,该方法通过传递一个驱动变量实现了一类分数阶混沌系统的修正投影同步,由于只需在驱动系统和响应系统之间传递一个驱动变量,具有较高的实用价值,最后以分数阶统一混沌系统为例进行了数值仿真,理论和数值仿真表明了该方法的有效性.     

基于参数切换算法的混沌系统吸引子近似及其电路设计

基于参数切换算法和离散混沌系统, 设计一种新的混沌系统参数切换算法, 给出了两算法的原理. 采用混沌吸引子相图观测法, 研究了不同算法下统一混沌系统和Rössler混沌系统参数切换结果, 最后引入方波发生器, 设计了Rössler混沌系统参数切换电路. 结果表明, 采用参数切换算法可以近似出指定参数下的系统, 其吸引子与该参数下吸引子一致; 基于离散系统的参数切换结果更为复杂, 当离散序列分布均匀时, 只可近似得到指定参数下的系统; 相比传统切换混沌电路, 参数切换电路不用修改原有系统电路结构, 设计更为简单, 输出结果受方波频率影响, 通过加入合适频率的方波发生器, 数值仿真与电路仿真结果一致.     

Detecting chaos in fractional-order nonlinear systems using the smaller alignment index

The identification between chaos and ordered states in fractional-order chaotic systems is a challenge as well as a hot topic due to the complex of fractional calculus. In this paper, the smaller alignment index (SALI) is developed to detect chaos in the fractional-order chaotic systems by introducing the fractional-order tangent systems. Numerical simulations are carried out based on the fractional-order simplified Lorenz system and the fractional-order Hénon map, which are continuous chaotic system and discrete chaotic system, respectively. It shows that the proposed method is effective for distinguishing chaos and order in different kinds of fractional-order chaotic systems.     

离子迁移忆阻混沌电路及其在语音保密通信中的应用

忆阻器是一种具有记忆功能和纳米级尺寸的非线性元件, 作为混沌系统的非线性部分, 能够使系统的物理尺寸大大减小, 同时可以得到各种丰富的非线性曲线, 提高混沌系统的复杂度和信号的随机性. 因此, 本文采用离子迁移忆阻器的磁控模型设计了一个新的混沌系统. 通过理论推导、数值仿真、Lyapunov指数谱、分岔图和Poincaré截面图研究了系统的基本动力学特性, 并分析了改变不同参数时系统动力学行为的变化. 同时, 建立了模拟该系统的SPICE电路, SPICE仿真结果与数值分析相符, 从而验证该混沌系统的混沌产生能力. 最后, 利用线性反馈同步控制方法实现了新构造的离子迁移忆阻混沌系统的同步, 并且采用该同步方法有效实现了语音信号的保密通信. 数值仿真证实了新混沌系统的存在性以及同步控制应用的可行性.     

Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.     

Reduced-order anti-synchronization of the projections of the fractional order hyperchaotic and chaotic systems

The article aims to study the reduced-order anti-synchronization between projections of fractional order hyperchaotic and chaotic systems using active control method. The technique is successfully applied for the pair of systems viz., fractional order hyperchaotic Lorenz system and fractional order chaotic Genesio-Tesi system. The sufficient conditions for achieving anti-synchronization between these two systems are derived via the Laplace transformation theory. The fractional derivative is described in Caputo sense. Applying the fractional calculus theory and computer simulation technique, it is found that hyperchaos and chaos exists in the fractional order Lorenz system and fractional order Genesio-Tesi system with order less than 4 and 3 respectively. The lowest fractional orders of hyperchaotic Lorenz system and chaotic Genesio-Tesi system are 3.92 and 2.79 respectively. Numerical simulation results which are carried out using Adams-Bashforth-Moulton method, shows that the method is reliable and effective for reduced order anti-synchronization.     

基于忆阻器的多涡卷混沌系统及其脉冲同步控制

忆阻器是一种具有记忆功能和纳米级尺寸的非线性元件,作为混沌系统的非线性部分,能够提高混沌系统的信号随机性和复杂度.本文基于增广Lü系统设计了一个三维忆阻混沌系统.仅仅通过改变系统的一个参数,该系统能产生单涡巻、双涡卷和四涡巻的混沌吸引子,说明该系统具有丰富的混沌特性.首先对该忆阻混沌系统的基本动力学行为进行了理论分析和数值仿真,如平衡点稳定性、对称性,Lyapunov指数和维数,分岔图和Poincare截面等.同时,建立了模拟该忆阻混沌系统的SPICE(simulation program with integrated circuit emphasis)电路,给出了不同参数下的电路实验相图,其仿真结果与数值分析相符,从而验证了该忆阻混沌系统的混沌产生能力.由于脉冲同步只在离散时刻传递信息,能量消耗小,同步速度快,易于实现单信道传输,因而在混沌保密通信中更具有实用性.因此,本文从最大Lyapunov指数的角度实现了该忆阻混沌系统的脉冲混沌同步,数值仿真证实了忆阻混沌系统的存在性以及脉冲同步控制的可行性,为进一步研究该忆阻混沌系统在语音保密通信和信息处理中的应用提供了实验基础.     

A KIND OF NEW AMPLIFIER

Chaotic characteristics in the iteration of logistic map(one-dimensional discrete dynamic system) are simulated and analyzed. The circuit implementation of a kind of chaotic amplifier model is based on the chaotic characteristics that chaos is sensitively dependent on its initial conditions, and the circuit simulation result is given using simulation program with integrated circuit emphasis for personal computer (PSPICE), and is compared with linear amplifier. Advantages and disadvantages of such a model are indicated.     

分数阶临界混沌系统及电路实验的研究

研究了分数阶临界混沌系统，设计了其分数阶电路结构.通过计算机仿真分析和电路实验，证实了分数阶临界混沌系统的混沌动力学行为. 关键词： 分数阶 临界混沌系统 电路     

一类多翼蝴蝶混沌吸引子及其电路实现

提出了一种构造多翼蝴蝶混沌吸引子的新方法,在Liu混沌系统的基础上,通过设计一种新的分段线性函数,构造了一个产生多翼蝴蝶混沌吸引子的混沌系统,对系统的平衡点、Lyapunov指数谱、分岔图、相图、频谱和Poincare截面进行了分析。最后,设计了相应的硬件电路,电路实验结果与数值仿真结果一致,验证了该方法的可行性和有效性。     

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。     

Chaotic attractors in incommensurate fractional order systems

In this paper, based on the stability theorems in fractional differential equations, a necessary condition is given to check the existence of 1-scroll, 2-scroll or multi-scroll chaotic attractors in a fractional order system. This condition is proposed for incommensurate order systems in general, but in the special case it converts to the condition given in the previous works for the commensurate fractional order systems. Though the presented condition is only a necessary (and not sufficient) condition for the existence of chaos it can be used as a powerful tool to distinguish for what parameters and orders of a given fractional order system, chaotic attractors can not be observed and for what parameters and orders, the system may generate chaos. It can also be used as a tool to confirm or reject results of a numerical simulation. Some of the numerical results reported in the previous literature are confirmed by this tool.     

分数阶共轭Chen混沌系统中的混沌及其电路实验仿真

研究了分数阶共轭Chen混沌系统的混沌行为, 给出了分数阶共轭Chen系统存在混沌吸引子的必要条件. 并设计了一种传递函数的新电路单元用来实现分数阶共轭Chen混沌系统, 利用Multisim2001电子工作平台进行了电路实验仿真. 数值模拟和电路实验仿真结果相符, 证实了分数阶共轭Chen系统确实存在混沌现象和所设计电路单元的有效性. 关键词： 分数阶 共轭Chen混沌系统 电路单元 电路仿真     

基于Chua电路的四维超混沌忆阻电路

近年来,忆阻混沌电路受到国内外学者的广泛关注,然而目前四维忆阻系统往往只存在普通混沌(仅有一个正Lyapunov指数),本文通过用忆阻替换Chua电路中电阻的新途径,得出一个简单的四维忆阻电路,与仅含有限个孤立不稳定平衡点的大多已知系统不同,本系统存在无穷多个稳定和不稳定平衡点,研究发现该系统存在着极限环、混沌、超混沌等丰富的复杂行为,通过进一步数值分析和电路仿真实验,证实了超混沌吸引子的存在,从而解决了关于四维忆阻电路是否存在超混沌的疑问。