The 0-1 test algorithm for chaos and its applications

To determine whether a given deterministic nonlinear dynamic system is chaotic or periodic,a novel test approach named zero-one (0-1) test has been proposed recently.In this approach,the regular and chaotic motions can be decided by calculating the parameter K approaching asymptotically to zero or one.In this study,we focus on the 0-1 test algorithm and illustrate the selection of parameters of this algorithm by numerical experiments.To validate the reliability and the universality of this algorithm,it is applied to typical nonlinear dynamic systems,including fractional-order dynamic system.     

An Image Encryption Approach Using a Shuffling Map

A new image encryption approach is proposed. First, a sort transformation based on nonlinear chaotic algorithm is used to shuffle the positions of image pixels. Then the states of hyper-chaos are used to change the grey values of the shuffled image according to the changed chaotic values of the same position between the above nonlinear chaotic sequence and the sorted chaotic sequence. The experimental results demonstrate that the image encryption scheme based on a shuffling map shows advantages of large key space and high-level security. Compared with some encryption algorithms, the suggested encryption scheme is more secure.     

Controlling chaos using Takagi--Sugeno fuzzy model and adaptive adjustment

In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi--Sugeno (TS) fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control from Lyapunov stability theory. The proposed approach offers a systematic design procedure for stabilizing a large class of chaotic systems in the literature about chaos research. The simulation results on R\"{o}ssler's system verify the effectiveness of the proposed methods.     

Global adaptive synchronization of chaotic systems with uncertain parameters

We propose a novel adaptive synchronization method for a class of nonlinear chaotic systems with uncertain parameters.Using the chaos control method,we derive a synchronizer,which can make the states of the driven system globally track the states of the drive system asymptotically.The advantage of our method is that our problem sctting is more general than those that already exist,and the synchronizer is simply constructed by an analytic formula,without knowledge in advance of the unknown bounds of the uncertain parameters.A computer simulation example is given to validate the proposed approach.     

Robust Blind Adaptive Channel Equalization in Chaotic Communication Systems

Based on the bounded property and statistics of chaotic signal and the idea of set-membership identification, we propose a set-membership generalized least mean square （SM-GLMS） algorithm with variable step size for blind adaptive channel equalization in chaotic communication systems. The steady state performance of the proposed SM-GLMS algorithm is analysed, and comparison with an extended Kalman filter （EKF）-based adaptive algorithm and variable gain least mean square （VG-LMS） algorithm is performed for blind adaptive channel equalization. Simulations show that the proposed SM-GLMS algorithm can provide more significant steady state performance improvement than the EKF-based adaptive algorithm and VG-LMS algorithm.     

Finite-time sliding mode synchronization of chaotic systems

A new finite-time sliding mode control approach is presented for synchronizing two different topological structure chaotic systems. With the help of the Lyapunov method, the convergence property of the proposed control strategy is discussed in a rigorous manner. Furthermore, it is mathematically proved that our control strategy has a faster convergence speed than the conventional finite-time sliding mode control scheme. In addition, the proposed control strategy can ensure the finite-time synchronization between the master and the slave chaotic systems under internal uncertainties and external disturbances. Simulation results are provided to show the speediness and robustness of the proposed scheme. It is worth noticing that the proposed control scheme is applicable for secure communications.     

Control of Unknown Chaotic Systems Based on Neural Predictive Control

We introduce the predictive control into the control of chaotic system and propose a neural network control algorithm based on predictive control. The proposed control system stabilizes the chaotic motion in an unknown chaotic system onto the desired target trajectory. The proposed algorithm is simple and its convergence speed is much higher than existing similar algorithms. The control system can control hyperchaos. We analyze the stability of the control system and prove the convergence property of the neural controller. The theoretic derivation and simulations demonstrate the effectiveness of the algorithm.     

Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.     

A Noise Cleaning Method for Chaotic Time Series and Its Application in Communication

A new algorithm for filtering highly noisy contaminated chaotic time series is proposed and realized. It is indicated by computer simulation that this algorithm can effectively reduce noise on chaotic signal no mater how parameter of chaos generator varies with time. In comparison with the extended-Kalman-filter-based method, this algorithm has a better filtering performance in the case of low signal-to-noise (SNR) ratios, and has the similar performance in the case of high SNR. In addition, a chaotic modulation communication system is also used to evaluate the performance of the algorithm, the result shows the effectiveness of the method.     

The open-plus-closed loop （OPCL） method for chaotic systems with multiple strange attractors

Based on the open-plus-closed-loop (OPCL) control method a systematic and comprehensive controller is presented in this paper for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). Results show that the final structure of the suggested controller for stabilization has a simple linear feedback form. To keep the integrity of the suggested approach, the globality proof of the basins of entrainment is also provided. In virtue of the OPCL technique, three different kinds of chaotic controls of the system are investigated, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one; and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the proposed means.     

基于混沌的自嵌入安全水印算法

利用混沌系统的伪随机性和初值敏感性，提出一种基于混沌的自嵌入安全水印算法.该算法以混沌初值为密钥生成混沌序列，根据混沌序列的索引有序序列随机生成图像块的水印嵌入位置.与现有的自嵌入算法相比，该算法实现了水印嵌入位置的随机选取，有效扩大了算法的密钥空间，且解决了自嵌入水印算法如何准确定位篡改块的问题.理论分析和仿真结果表明，该算法不仅提高了自嵌入水印算法的篡改定位的能力，而且进一步增强了算法抵抗向量量化攻击和同步伪造攻击的能力. 关键词： 数字水印 混沌 脆弱水印 自嵌入     

A robust steganographic technique based on improved chaotic-range systems

This paper presents a novel chaos-based technique of steganography in spatial domain. In the last decade, chaos theory has gained utmost importance in multimedia security applications. Generally, 1-D chaotic maps are employed because of computational ease and structural simplicity but their limited chaotic range is an obstacle. In the proposed work, we model the nonlinear combinations of 1-D chaotic maps. These chaotic systems possess chaotic behavior throughout the domain. We, for the first time, propose an effective application of these improved chaotic systems in steganography. These newly synthesized systems are used to embed secret information in the least significant bits (LSBs) of the host image. By comparing with some recent models, we prove that involving improved chaotic systems in steganographic approach really produces extraordinary outcomes. We determine the strength of our steganographic algorithm through the most significant statistical analyses such as information entropy, correlation, contrast, energy, homogeneity, peak signal to noise ratio (PSNR) and mean square error (MSE). We further prove the robustness of the anticipated technique against several image processing attacks. The upshot of these analysis techniques shows that our algorithm is highly reliable and produces coherent results.     

混沌信号的压缩感知去噪

对非线性时间序列进行噪声抑制是从中提取有效信息的前提. 混沌信号的去噪算法不仅要使滤波后的信号具有较高的信噪比, 也要具有较好的不确定性. 从压缩感知的角度出发,提出了一种新的噪声抑制方法. 该方法包括估计噪声方差, 以及依据动态的稀疏度将观测值往确定的过完备字典上投影. 仿真实验表明, 该方法比常用的小波阈值法和局部曲线拟合法具有更高的输出信噪比, 而原始信号的混沌特性也能得到较大程度的恢复.     

A New Approach for Controlling Chaos Based on Direct Optimizing Predictive Control

We introduce the predictive control theory into the study of chaos control and propose a direct optimizing predictive control algorithm based on a neural network model. The proposed control system stabilizes the chaotic motion in an unknown chaotic system onto the desired target trajectory. Compared with the existing similar algorithms, the proposed control system has faster response, so it requires much shorter time for the stabilization of the chaotic systems.The proposed approach can control hyperchaos and the algorithm is simple. The convergence of the control algorithm and the stability of the control system can be guaranteed. The theoretic analysis and simulations demonstrate the effectiveness of the algorithm.     

Biological image processing via Chaotic Differential Search and lateral inhibition

In this paper, we propose a hybrid biological image processing approach, which is based on Chaotic Differential Search (CDS) algorithm and lateral inhibition (LI) mechanism. We named this hybrid biological image processing approach as LI-CDS. Differential Search (DS) algorithm is a new bio-inspired optimization algorithm mimicking the migration behavior of an organism, and has been successfully used for solution of coordinate system transformation. The property of chaotic variable is integrated into DS to improve its search strategy so that it can escape from the local optimum. Furthermore, lateral inhibition mechanism, which is verified to have good effects on image edge extraction and image enhancement, is employed to pre-process images involved. In this hybrid biological image processing mechanism, our proposed LI-CDS method incorporates both advantages of chaos theory and lateral inhibition mechanism. Series of comparative experimental results by using LI-CDS, DS, CDS and Particle Swarm Optimization (PSO) demonstrate that the proposed LI-CDS performs better than the other three methods.     

New quantum algorithm for studying NP-complete problems

Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm which is a combination of the ordinary quantum algorithm with a chaotic dynamical system. We consider the satisfiability problem as an example of NP-complete problems and argue that the problem, in principle, can be solved in polynomial time by using our new quantum algorithm.     

基于混合交叉进化算法的混沌系统参数估计

提出一种混合交叉进化算法 来估计混沌系统的未知参数. 首先通过构造一个适当的适应度函数, 将混沌系统的参数估计问题转化为一个多维的优化问题. 在混合交叉进化算法中, 利用佳点集方法初始化种群, 增加了算法的稳定性和全局搜索能力. 在进化过程中, 混合交叉操作既能指导种群个体向最优解子空间靠近, 又能提高算法跳出局部最优的能力, 从而协调了算法的勘探和开采能力. 以几个标准测试函数和典型的Lorenz混沌系统为例进行仿真实验, 结果表明了该方法的有效性.     

基于Min-Max方法的混沌系统采样同步控制研究

针对含有扰动的混沌系统, 设计采样同步控制器, 利用输入时滞法将含有采样同步控制器的混杂系统转换为具有输入时滞的连续系统. 并考虑对系统影响最坏的干扰程度, 在该种情况下, 基于线性矩阵不等式(LMI)技术和min-max鲁棒控制方法, 给出了使误差系统稳定的充分条件, 确保混沌系统在所容许的扰动下均能实现完全同步. 仿真结果说明所设计的采样同步控制方案具有很强的鲁棒性, 适合应用于保密通信系统中. 关键词： 混沌同步 采样控制 min-max方法 输入时滞     

动力学变换法探测连续系统不稳定周期轨道

本文利用动力学变换方法和庞加莱截面方法对两种连续混沌动力学系统进行不稳定周期轨道探测研究, 并对Lorenz系统进行了替代数据法检验.结果表明:基于庞加莱截面的动力学变换改进算法 可有效探测连续混沌动力学系统中的不稳定周期轨道.