基于多目标遗传算法的8×8 S盒的优化设计方法

混沌系统具有非线性、伪随机性、初始值敏感等特性,为基于动力系统构造性能良好的S盒提供了基础,进一步保证了分组加密算法安全性.目前,基于混沌构造S盒的方法大多数针对单个性能指标进行优化,难以获得全面的性能提升.针对此问题,结合混沌映射与多目标遗传算法,提出了一种新的S盒设计方法.首先,利用混沌映射的特性产生初始S盒种群;然后,以S盒的非线性度和差分均匀性为优化目标,基于遗传算法框架对上述两指标进行优化.针对S盒的特点,在优化算法中引入了交换操作,设计了新的变异操作以及非支配序集计算,有效提升了S盒的非线性度和差分均匀性.实验结果表明该算法产生的S盒其差分均匀度为6,非线性度值至少为110,有效提升了S盒的综合性能.

Hyperchaos evolved from the Liu chaotic system

This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.

Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control

Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.

Chaotic Motion Analysis for a Coupled Magnetic-Flow-Mechanical Model of the Rectangular Conductive Thin Plate

The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin plate theory,considering geometric nonlinearity and using the principle of virtualwork,the nonlinearmotion partial differential equation of the rectangular conductive thin plate is deduced.Using the separate variable method and Galerkin’s method,the system motion partial differential equation is converted into the general equation of the Duffing equation;the Hamilton system is introduced,and the Melnikov function is used to analyze the Hamilton system,and obtain the critical surface for the existence of chaos.The bifurcation diagram,phase portrait,time history response and Poincarémap of the vibration system are obtained by numerical simulation,and the correctness is demonstrated.The results showthatwhen the ratio of external excitation amplitude to damping coefficient is higher than the critical surface,the system will enter chaotic state.The chaotic motion of the rectangular conductive thin plate is affected by different magnetic field distributions and airflow.

具有稚虫迁徙机制的S型自适应混沌蜉蝣算法

针对蜉蝣优化算法(MA)全局搜索能力较弱,对子代优秀个体有效信息利用不够充分的缺点,以及在计算中后期易陷入局部收敛,进而影响优化效果的问题,提出一种具有稚虫迁徙机制的S型自适应混沌蜉蝣优化算法(S-AMA)。S-AMA算法首先采用Logistic混沌映射产生蜉蝣种群,增加算法初期种群的多样性;随后,将蜉蝣生命周期进行数学建模,并引入S型生命系数替换原有的重力惯性系数,动态调整算法探索能力和开发能力间的平衡性;最后,根据蜉蝣在缺氧环境下的种群活动,引入稚虫迁徙机制强化子代优秀个体摆脱局部最优的能力,进而更加充分地搜索最优解附近的区域,以增强算法的收敛精度。实验部分将S-AMA应用于标准函数测试集,并分别进行优化对比实验、Wilcoxon秩和检验。结果表明:与对比算法相比,S-AMA算法具有更好的寻优能力、收敛速度及鲁棒性。

A self-adaptive synchronization controller for Liu chaotic systems

A kind of synchronization controller for Liu chaotic systems whose nonlinear components are subject to Lipschitz condition was proposed. By using Lyapunov function and linear matrix inequality technique, a self-adaptive synchronization controller was constructed for Liu chaotic systems. There are two components of our derived synchronization controller: linear and nonlinear component. Linear component is composed of errors of the state variables between driving-systems and responding-stems, and nonlinear component is a self-adaptive synchronization controller. a proof was given for proving the feasibility of this method, and numerical simulations of Liu chaotic systems show its effectiveness. Furthermore, this method can be applied to other chaotic systems, such as Chen systems, Lorenz systems, Chua systems and Rssler systems,etc.

Controlling Liu Chaotic System with Feedback Method and Its Circuit Realization

In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various attractors are demonstrated not only by numerical simulations but also by circuit experiments. Only one feedback channel is used in our study, which is useful in communication. The circuit experiments show that our study has significance in practical applications.

Liu混沌系统基于T-S模糊模型的控制方法

论文运用并行分布补偿(PDC)技术建立了Liu混沌系统的T-S模型,并利用Lyapunov稳定性理论和线性矩阵不等式(LMIs)方法,设计了模糊控制器,仿真结果表明,所设计的控制器能有效地控制Liu混沌系统的混沌时间轨迹到其零平衡点,且控制简单可靠.

Liu-cos混沌系统在声波弱信号检测中的应用

针对混沌三维弱信号检测系统的特点,设计了一种傅里叶变换和李雅普诺夫算法相结合的收敛性判别算法,证明了三维Liu-cos混沌系统对于声波弱信号检测具有广域性并且当输入声波信号幅值大于临界阈值时,系统变量x输出平衡于输入的周期摄动力信号,系统变量y和z的输出收敛于零,临界阈值具有唯一性。解决了传统Duffing混沌系统应用于声波弱信号检测时,系统变量x和y输出不收敛、只能进入窄域检测等问题。构造了Duffing混沌系统和三维Liu-cos混沌系统的实际声波检测实验,分析了混沌系统在实际声波检测过程中的性能。

基于DSP的Liu混沌系统的实现

介绍了一种用DSP实现Liu混沌系统的方案.采用TMS320F2812和DA转换芯片TLC7528C作为工具,将Liu系统离散化后用DSP进行迭代计算,再进行DA转换,输出到示波器上得到相图,并与Matlab仿真结果比较,证明了该方法的正确性.使用该方法不仅观察到了数字电路中的混沌现象,应用到实际中还可与其他数字器件完好地对接,拓宽了混沌理论的应用领域.

Adaptive synchronization of a critical chaotic system

This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory,a novel adaptive control law is derived for the synchronization of a new chaotic system with known or unknown system parameters.Theoretical analysis and numerical simulations showthe effectiveness and feasibility of the proposed schemes.

A novel study on the impulsive synchronization of fractional-order chaotic systems

The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. The synchronization criterion is suitable for the case of the order 0 〈 q ≤ 1. It is more general than those of the known results. Simulation results are given to show the effectiveness of the proposed synchronization criterion.

Applying and Comparison of Chaotic-Based Permutation Algorithms for Audio Encryption

This research presents,and claries the application of two permutation algorithms,based on chaotic map systems,and applied to a le of speech signals.They are the Arnold cat map-based permutation algorithm,and the Baker’s chaotic map-based permutation algorithm.Both algorithms are implemented on the same speech signal sample.Then,both the premier and the encrypted le histograms are documented and plotted.The speech signal amplitude values with time signals of the original le are recorded and plotted against the encrypted and decrypted les.Furthermore,the original le is plotted against the encrypted le,using the spectrogram frequencies of speech signals with the signal duration.These permutation algorithms are used to shufe the positions of the speech les signals’values without any changes,to produce an encrypted speech le.A comparative analysis is introduced by using some of sundry statistical and experimental analyses for the procedures of encryption and decryption,e.g.,the time of both procedures,the encrypted audio signals histogram,the correlation coefcient between specimens in the premier and encrypted signals,a test of the Spectral Distortion(SD),and the Log-Likelihood Ratio(LLR)measures.The outcomes of the different experimental and comparative studies demonstrate that the two permutation algorithms(Baker and Arnold)are sufcient for providing an efcient and reliable voice signal encryption solution.However,the Arnold’s algorithm gives better results in most cases as compared to the results of Baker’s algorithm.

Ergodic sensitivity analysis of one-dimensional chaotic maps

Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view.In this work,we present a numerical investigation of a novel approach,known as the space-split sensitivity or S3 algorithm.The S3 algorithm is an ergodic-averaging method to differentiate statistics in ergodic,chaotic systems,rigorously based on the theory of hyperbolic dynamics.We illustrate S3 on one-dimensional chaotic maps,revealing its computational advantage over na?ve finite difference computations of the same statistical response.In addition,we provide an intuitive explanation of the key components of the S3 algorithm,including the density gradient function.

Chaotic synchronization via linear controller

A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascade-connected system is presented. Based on the method developed in the paper, two simple and linear feedback controllers, as examples, are derived for the synchronization of Liu chaotic system and Duffing oscillator, respectively. This method is quite flexible in constructing a control law. Its effectiveness is also illustrated by the simulation results.

Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lya-punov＇s stability theory, linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an Hoe-norm constraint. Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.

Chaotic behavior learning of Chua's circuit

Least-square support vector machines（LS-SVM） are applied for learning the chaotic behavior of Chua＇s circuit.The system is divided into three multiple-input single-output（MISO） structures and the LS-SVM are trained individually.Comparing with classical approaches,the proposed one reduces the structural complexity and the selection of parameters is avoided.Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation.Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua＇s circuit state variables,and exhibit the chaotic attractors under the autonomous working mode.

Hurst’s Memory for Chaotic, Tree Ring, and SOI Series

Hurst’s memory that roots in early work of the British hydrologist H.E. Hurst remains an open problem in stochastic hydrology. Today, the Hurst analysis is widely used for the hydrological studies for the memory and characteristics of time series and many methodologies have been developed for the analysis. So, there are many different techniques for the estimation of the Hurst exponent (H). However, the techniques can produce different characteristics for the persistence of a time series each other. This study uses several techniques such as adjusted range, rescaled range (RR) analysis, modified rescaled range (MRR) analysis, 1/f power spectral density analysis, Maximum Likelihood Estimation (MLE), detrended fluctuations analysis (DFA), and aggregated variance time (AVT) method for the Hurst exponent estimation. The generated time series from chaos and stochastic systems are analyzed for the comparative study of the techniques. Then, this study discusses the advantages and disadvantages of the techniques and also the limitations of them. We found that DFA is the most appropriate technique for the Hurst exponent estimation for both the short term memory and long term memory. We analyze the SOI (Southern Oscillations Index) and 6 tree-ring series for USA sites by means of DFA and the BDS statistic is used for nonlinearity test of the series. From the results, we found that SOI series is nonlinear time series which has a long term memory of H = 0.92. Contrary to earlier work, all the tree ring series are not random from our analysis. A certain tree ring series show a long term memory of H = 0.97 and nonlinear property. Therefore, we can say that the SOI series has the properties of long memory and nonlinearity and tree ring series could also show long memory and non-linearity.

Design of strong S-boxes based on spatiotemporal chaotic system

A substitution box (S-box) plays an important role in cryptographic algorithms.The design of S-box using chaotic systems has attracted a great deal of attention in recent years.A new method for obtaining cryptographically strong S-boxes based on spatiotemporal chaotic system is proposed in this paper.The discretized Baker map and affine transformation are used orderly by an algorithm to shuffle the table generated by the spatiotemporal chaotic system.The cryptographical properties of these S-boxes such as bijection,nonlinearity,strict avalanche,output bits independence and equiprobable input /output XOR distribution are analyzed.The results of numerical analysis show that the S-box designed by this method can against several attacks and all the criteria for designing good S-box can be satisfied approximately.More strong S-boxes can be obtained by this method with the change of the original conditions or control parameters of the spatiotemporal chaos system.Furthermore,our approach is suitable for practical application in designing cryptosystem.

TCM Treatment of Asthma in Children with Yin Hua Wu Mei Tang——Professor Liu Bichen's Experience in Treating Asthma

Asthma is characterized by paroxysmaldyspnea,rales in the throat,difficulty in breathing,and inability to lie horizontally.It is commonly seenin children with a weak body constitution,and tendsto be intractable,thus being harmful to the