Complicated Attractor and Novel Route to Chaos via Cubic Nonlinearity Controller

By introducing a nonlinear state feedback controller, a complicated chaotic attractor of fourdimensional continuous autonomous chaotic system evolved from Lorenz system is proposed. The controller consists of a cubic cross-product term of three variables and a self variable term with control parameter. This paper verifies that the proposed system has complex dynamical behavior, which can evolve into periodic and chaotic behavior cyclically. These circular routes to chaos have self-similar bifurcation structure in a wide parameter variation range. An electronic circuit is designed to demonstrate the complicated attractor.     

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。     

A non-autonomous chaotic system with no equilibrium

Recently, researchers showed that adding a stepwise control pulse to the Sprott C system (with two equilibrium points) can create a translational multi-butterfly attractor. In this research, a sinusoidal control pulse is added to a system with no equilibria. So, a non-autonomous chaotic system with no equilibria is designed and studied. The sinusoidal term causes an extension in the chaotic attractor. Dynamical behaviors of the proposed oscillator are studied. Bifurcation analysis by changing the frequency of the sinusoidal term shows its unbounded solution at some parameters. Also, bifurcation diagram of the oscillator by the force's strength is studied. Lyapunov exponents show that the oscillator has chaotic dynamics in the entire studied interval of force's strength. In addition, circuit implementation shows its feasibility.     

一个新的超混沌系统及其电路实现

通过对一个光滑三维二次混沌系统上引入一个新的状态反馈控制器,构造出一个新的四维超混沌系统。详细地分析了该系统平衡点的性质、超混沌吸引子相图、Lyapunov指数和分岔图等基本动力学特性。数值模拟结果表明,新的四维系统能随着参数变化呈现出周期态、拟周期态、混沌态和超混沌态等丰富的动力学行为。最后设计了硬件电路实验,也很好的证实了相关结果。     

混沌频率调制系统设计

针对混沌调制系统中存在相图信息泄密的问题,文中提出了基于混沌参数调制模型设计混沌频率调制系统的方法。该方法利用预传信号作为调制信号,调制混沌系统中特定的参数,使加载信息的混沌信号仅产生频谱分布上的变化,而信号的吸引子位置特性不随时间发生变化,同时文中也给出了基于误差检测的信号解调方法。通过证明及实验仿真,该系统实现了对连续信号的混沌频率调制,并有效地消除了混沌信号在相图中的分叉现象,以及提高了混沌调制系统的安全性能。     

一个切换混沌系统的分析与电路实现

采用改变系统乘积项的方法,在已提出的混沌系统的基础上,构建了一个切换混沌系统。分析了平衡点的性质,混沌吸引子相图和Lyapunov指数等特性,设计了可实现切换混沌系统的电路并进行了电路实验,实现结果与仿真结果一致：     

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...     

一种基于超混沌Mackey-Glass系统的语音加密算法

针对低维混沌序列加密语音信号保密性较差,而复合混沌序列加密信息又使得混沌系统难以用软硬件实现的问题,研究了一种基于参数辨识的超混沌时滞模型的加密算法.该算法引入了分块加密的思想,采用了一种映射的方法产生密钥,不仅实现简单,实用性强,而且有效地改善了由于计算机有限精度效应而产生的混沌周期行为,增强了保密性能.     

A no-equilibrium memristive system with four-wing hyperchaotic attractor

A new memristive system is proposed in this paper which can have no equilibrium and a line of equilibrium based on the value of its controlling parameter. Also, changing that parameter can cause the system having both chaotic and hyperchaotic solutions. This system has a multi-wing strange attractor. Dynamical properties of this system such as Lyapunov exponents and bifurcation diagram are calculated. This system belongs to the category of systems with hidden and multistable attractors. A system with all the above-mentioned properties is not common in the literature. Finally, an adaptive sliding mode control method is applied to synchronize this chaotic system.     

Chaos generation in fractional-order switched systems and its digital implementation

A double-scroll chaotic attractor generated by a fractional-order switched system is presented. Based on unstable dissipative systems (UDS) and a switching law, a fractional-order UDS is proposed. Chaos behavior is found with a fractional order as low as 2.568 by satisfying the stability criterion for fractional order chaotic systems. The fractional-order switched system is transformed to an equivalent switched system with augmented states. Then, the equivalent system is straightforward implemented on an ARM system-on-chip board by using Python high level programming language. Numerical simulations are in good agreement with experimental results, which demonstrates the usefulness of proposed method. Additionally, the test 0–1 and a chaos definition for finite state sets are given to demonstrate chaotic behavior. Finally, a random number generator is also proposed as a possible application.     

Synchronization of Chaotic Systems Using Time-Delayed Fuzzy State-Feedback Controller

This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult. To investigate the system stability and facilitate the design of fuzzy controller, Takagi-Sugeno (T-S) fuzzy models are employed to represent the system dynamics of the chaotic systems. Furthermore, the membership grades of the T-S fuzzy models become uncertain due to the existence of parameter uncertainties which further complicates the system analysis. To ease the stability analysis and produce less conservative analysis result, the membership functions of both T-S fuzzy models and fuzzy controller are considered. Stability conditions are derived using Lyapunov-based approach to aid the design of fuzzy state-feedback controller to synchronize the chaotic systems. Simulation examples are presented to illustrate the merits of the proposed approach.     

忆阻开关混沌电路及其吸引子共存现象研究

为了研究忆阻开关电路的动力学行为,该文提出一种具有多吸引子共存现象的忆阻开关混沌电路。在该电路中存在多吸引子分岔,当系统中发生边界碰撞之后,系统中将产生不同的吸引子共存现象。其中包括单周期极限环与混沌吸引子共存,不同的混沌吸引子共存,对称的2周期极限环共存现象,以及对称的2周期极限环与5周期极限环共存现象等。该文通过相图、分岔图等数值仿真,分析了该电路的动力学行为,并利用PSIM电路仿真验证了其电路的可行性,对开关电路中多吸引子共存现象和混沌应用的研究具有重要意义。     

A novel memristive chaotic system without any equilibrium point

Various chaotic systems have been studied recently. They can show many different dynamics and features. A memristive 4D chaotic oscillator with no equilibria, multistability, and hidden attractor is presented in this paper. Chaotic attractor of the proposed oscillator is discussed, and its dynamical behaviors are investigated. The oscillator does not have any equilibrium. In addition, the phenomena of multistability is studied in this system. It shows chaotic dynamics and periodic windows, verified by Lyapunov exponents’ diagram. Image encryption is studied as an engineering application of the system. The proposed system has a proper performance in encryption. Finally, this memristive chaotic system is realized using FPGA.     

一种可完全线性化的不同类型混沌系统同步方法

讨论可完全线性化的不同类型混沌系统之间的同步问题.根据滑模控制原理求取混沌同步控制形式,利用扩张状态观测器对系统信息进行渐进估计,把复杂的滑模控制策略变为可实现的控制方式,以此实现具有不确定性混沌系统的同步.以Duffing和Vander Pol系统为例进行仿真,效果良好.     

基于量子混沌粒子群优化算法的分数阶超混沌系统参数估计

为了对分数阶超混沌系统中的未知参数进行准确估计,提出一种量子混沌粒子群优化算法（Quantum chaos particle swarm optimization,QCPSO）.该算法通过对量子粒子群优化算法（Quantum behaved particle swarm optimization,QPSO）的实现机理进行分析,并结合量子纠缠与混沌系统之间的相关性而实现.首先,将量子势阱中心视为混沌吸引子围绕的不动点,处于吸引子外部的粒子会逐渐聚集于吸引子之内,而处于吸引子内部的粒子会出现快速分离扩散的现象;然后,采用基于随机映射的粒子更新机制,充分保证混沌粒子的初值多样性;最后,提出了基于不动点中心的尺度自适应策略,解决了算法后期的搜索停滞问题.运用QCPSO算法对典型分数阶超混沌系统参数进行估计,结果表明,该算法在收敛速度与精度上优于改进的差分进化算法、自适应人工蜂群算法以及改进的量子粒子群优化算法.     

具有噪声扰动的统一混沌系统的同步控制

研究了一类具有噪声扰动的统一混沌系统的同步控制问题。基于滑模变结构控制理论,提出了利用不确定性观测器估计扰动噪声,用噪声的观测值来设计控制器的新方法,而且适当选取观测器反馈增益可以使观测误差充分的小,从而可得到几乎没有受到扰动时的控制效果。和常规滑模变结构控制方法相比,所设计的控制器既能有效地抑制抖振,又能降低控制器参数设计的保守性。最后,基于Matlab 6.5软件对Lorenz混沌系统进行分析和数值模拟,验证了该滑模控制方法在混沌同步中的优良性能。     

Globally Exponential Synchronization and Parameter Regulation for Coupled Chaotic System via Adaptive Control

Based on Lyapunov stability theory,an adaptive controller is designed for a class of chaotic systems. Globally exponential synchronization and parameter regulation for couple chaotic systems can be carried out simultaneously. The controller and the regulating law of parameters are directly constructed by analytic formula. Simulation results with some chaotic systems show the effectiveness of the proposed controller.     

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...     

Inversion-free force tracking control of piezoelectric actuators using fast finite-time integral terminal sliding-mode

The major hurdles to control the force created by piezoelectric actuators (PEAs) are originated from its strong nonlinear behaviors which include hysteresis, creep, and vibration dynamics. To achieve an accurate, fast and robust force tracking performance without using complicated modeling and parameter identification of PEAs, this paper presents a practical direct force control scheme. The proposed controller is based on two core approaches: 1) fast finite-time integral terminal sliding mode (FFI-TSM) which allows fast convergence and high accuracy to the closed-loop system without control chattering; and 2) an inverse-model-free compensation, named force-based time-delayed estimation (FBTDE) which offers significant robustness with minimum use of plant dynamics information. The finite-time stability of the overall closed-loop system is proven through the Lyapunov’s method. The proposed force tracking controller is implemented on the PEA system driving a variable physical damping actuator mechanism. The overall accuracy, convergence speed, and robustness of the proposed controller are validated under various experimental scenarios. Comparative experimental results are particularly presented to verify the effectiveness of the FFI-TSM term and the FBTDE term.     

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.