Describing Chaos of Continuous Time System Using Bounded Space Curve

The qualitative solutions of dynamical system expressed with nonlinear differential equation can be divided into two categories. One is that the motion of phase point may approach infinite or stable equilibrium point eventually. Neither periodic excited source nor self-excited oscillation exists in such nonlinear dynamic circuits, so its solution cannot be treated as the synthesis of multiharmonic. And the other is that the endless vibration of phase point is limited within certain range, moreover possesses character of sustained oscillation, namely the bounded nonlinear oscillation. It can persistently and repeatedly vibration after dynamic variable entering into steady state;moreover the motion of phase point will not approach infinite at last;system has not stable equilibrium point. The motional trajectory can be described by a bounded space curve. So far, the curve cannot be represented by concretely explicit parametric form in math. It cannot be expressed analytically by human. The chaos is a most universally common form of bounded nonlinear oscillation. A number of chaotic systems, such as Lorenz equation, Chua’s circuit and lossless system in modern times are some examples among thousands of chaotic equations. In this work, basic properties related to the bounded space curve will be comprehensively summarized by analyzing these examples.

A novel pseudo-random coupled LP spatiotemporal chaos and its application in image encryption

In this paper, first, we investigate a novel one-dimensional logistic-PWLCM（LP） modulation map which is derived from the logistic and PWLCM maps. Second, we propose a novel PCLML spatiotemporal chaos in pseudo-random coupling method that can accelerate the system behavior of the fully spatial chaos. Here, because the better chaotic properties include a wide range of parameter settings and better ergodicity than a logistic map, the LP is used in PCLML as f（x）. The Kolmogorov–Sinai entropy density and universality and the bifurcation diagram are employed to investigate the chaotic behaviors of the proposed PCLML model. Finally, we apply the LP and PCLML chaotic systems to image encryption to improve the effectiveness and security of the encryption scheme. By combining self-generating matrix model M and dynamic substitution box（S-Box） methods, we design a new image encryption algorithm. Numerical simulations and security analysis have been carried out to demonstrate that the proposed algorithm has a high security level and can efficiently encrypt several different kinds of images into random-like images.

A novel block encryption scheme based on chaos and an S-box for wireless sensor networks

The wireless sensor network （WSN） has been widely used in various fields, but it still remains in the preliminary discovery and research phase with a lack of various related mature technologies. Traditional encryption schemes are not suitable for wireless sensor networks due to intrinsic features of the nodes such as low energy, limited computation capability, and lack of storage resources. In this paper, we present a novel block encryption scheme based on the integer discretization of a chaotic map, the Feistel network structure, and an S-box. The novel scheme is fast, secure, has low resource consumption and is suitable for wireless sensor network node encryption schemes. The experimental tests are carried out with detailed analysis, showing that the novel block algorithm has a large key space, very good diffusion and disruptive performances, a strict avalanche effect, excellent statistical balance, and fast encryption speed. These features enable the encryption scheme to pass the SP800-22 test. Meanwhile, the analysis and the testing of speed, time, and storage space on the simulator platform show that this new encryption scheme is well able to hide data information in wireless sensor networks.

Chaos and Its Impulsive Control in Chua's Oscillator via Time-Delay Feedback

A novel framework for chaos and its impul-sive control in Chua＇s oscillator via time-delay feedback is presented.The exponential stability of impulsive control Chua＇s oscillator via time-delay feedback is considered,and some novel conditions are obtained.Then a novel impulsive controller design procedure is proposed.Simulation experiments are provided to demonstrate the feasibility and effectiveness of our method finally.

Parrondo's paradox for chaos control and anticontrol of fractional-order systems

We present the generalized forms of Parrondo＇s paradox existing in fractional-order nonlinear systems. The gener- alization is implemented by applying a parameter switching （PS） algorithm to the corresponding initial value problems associated with the fractional-order nonlinear systems. The PS algorithm switches a system parameter within a specific set of N 〉 2 values when solving the system with some numerical integration method. It is proven that any attractor of the concerned system can be approximated numerically. By replacing the words ＂winning＂ and ＂loosing＂ in the classical Parrondo＇s paradox with ＂order＂ and ＂chaos＂, respectively, the PS algorithm leads to the generalized Parrondo＇s paradox： chaos1 ＋ chaos2 ＋..- ＋ chaosN = order and order1 ＋ order2 ＋.-. ＋ orderN = chaos. Finally, the concept is well demon- strated with the results based on the fractional-order Chen system.

Generating Li-Yorke chaos in a stable continuous-time T-S fuzzy model via time-delay feedback control

This paper investigates the chaotification problem of a stable continuous-time T S fuzzy system. A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique. Then, the asymptotically approximate relationship between the controlled continuous-time T-S fuzzy system with time-delay and a discrete-time T-S fuzzy system is established. Based on the discrete-time T-S fuzzy system, it proves that the chaos in the discrete- time T-S fuzzy system satisfies the Li-Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem. Finally, the effectiveness of the proposed chaotic anticontrol method is verified by a practical example.

Impulsive control for synchronization of nonlinear Rossler chaotic systems

This paper reports that an impulsive control theory for synchronization of nonlinear Rossler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronizution law. The proposed impulsive control scheme is illustrated by nonlinear Rossler chaotic systems and the simulation results demonstrate the effectiveness of the method.

LMI-based output feedback fuzzy control of chaotic system with uncertainties

This paper studies the robust fuzzy control for nonlinear chaotic system in the presence of parametric uncertainties. An uncertain Takagi-Sugeno （T-S） fuzzy model is employed for fuzzy modelling of an unknown chaotic system. A sufficient condition formulated in terms of linear matrix inequality （LMI） for the existence of fuzzy controller is obtained. Then the output feedback fuzzy-model-based regulator derived from the LMI solutions can guarantee the stability of the closed-loop overall fuzzy system. The T-S fuzzy model of the chaotic Chen system is developed as an example for illustration. The effectiveness of the proposed controller design methodology is finally demonstrated through computer simulations on the uncertain Chen chaotic system.

Synchronising chaotic Chua's circuit using switching feedback control based on piecewise quadratic Lyapunov functions

This paper investigates the chaos synchronisation between two coupled chaotic Chua＇s circuits. The sufficient condition presented by linear matrix inequalities （LMIs） of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions （pwLDIs） model of synchronisation error dynamics, then we design a switching （piecewise-linear） feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results.

High-precision chaotic radial basis function neural network model:Data forecasting for the Earth electromagnetic signal before a strong earthquake

The Earth’s natural pulse electromagnetic field data consists typically of an underlying variation tendency of intensity and irregularities.The change tendency may be related to the occurrence of earthquake disasters.Forecasting of the underlying intensity trend plays an important role in the analysis of data and disaster monitoring.Combining chaos theory and the radial basis function neural network,this paper proposes a forecasting model of the chaotic radial basis function neural network to conduct underlying intensity trend forecasting by the Earth’s natural pulse electromagnetic field signal.The main strategy of this forecasting model is to obtain parameters as the basis for optimizing the radial basis function neural network and to forecast the reconstructed Earth’s natural pulse electromagnetic field data.In verification experiments,we employ the 3 and 6 days’data of two channels as training samples to forecast the 14 and 21-day Earth’s natural pulse electromagnetic field data respectively.According to the forecasting results and absolute error results,the chaotic radial basis function forecasting model can fit the fluctuation trend of the actual signal strength,effectively reduce the forecasting error compared with the traditional radial basis function model.Hence,this network may be useful for studying the characteristics of the Earth’s natural pulse electromagnetic field signal before a strong earthquake and we hope it can contribute to the electromagnetic anomaly monitoring before the earthquake.

Impulsive Control for T-S Fuzzy Model Based Chaotic Systems Consisting of Van der Pol Oscillators Coupled to Linear Oscillators

This paper proposes an impulsive control scheme for chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators （VDPL） based on their Takagi-Sugeno （T-S） fuzzy models. A T-S fuzzy model is utilized to represent the chaotic VDPL system. By using comparison method, a general asymptotical stability criterion by means of linear matrix inequality （LMI） is derived for the T-S fuzzy model of VDPL system with impulsive effects. The simulation results demonstrate the effectiveness of the proposed scheme.

Thomas Chao’s Journalistic Activities and Influence on Increasing China’s Voice Worldwide

In the 1930s and 1940s,Thomas Chao,an internationally-renowned Chinese journalist,influenced Chinese journalists’way of covering and writing news with his own prominent experience in international news reporting.Based on his long-term news practice,Chao analyzed the differences between Chinese and Western press and explored the way for improvement.He called on the government to set up a national news agency so as to establish itself in the field of international communication,and helped the Central News Agency to take back Reuters’right to publish in China.Chao also actively promoted the exchange and cooperation between Chinese newspapers and news agencies and foreign press in international communication activities,striving to increase China’s voice worldwide.

基于抗退化混沌系统和初等元胞自动机的动态S盒设计

S盒是多数分组密码算法的基本非线性模块,可以满足分组密码算法的混淆、扩散要求。为了提高混沌S盒的安全性,文中利用抗退化混沌系统生成S盒元素,基于初等元胞自动机生成S盒检索表的方式来生成S盒。抗退化混沌系统可以避免发生Skew Tent系统进入不动点的情况,消除低精度下系统进入短周期的现象。因为初等元胞自动机的迭代规则为二元域上的运算,且满足时空上的离散性,所以,将初等元胞自动机运用到混沌分组密码中时,不用考虑动力学退化的问题。当初等元胞自动机的迭代规则为全局混沌规则时,只要元胞个数足够,就可以保证输出的伪随机性。利用初等元胞自动机生成S盒的检索表,在保证S盒设计的混淆原则的同时还可以简化S盒的生成步骤。最后对所设计的S盒进行安全性分析对比,实验结果表明,所提方法生成的S盒具有良好的安全性,满足分组密码的混淆、扩散原则,可用于混沌分组密码算法设计中。

抵抗泄露攻击的无线传感器网络分组加密算法

混沌作为一种复杂的动力学系统,和密码学中的很多特性具有相似性。混沌内在的类随机特性对应于伪随机序列,混沌对初始条件和控制参数的极端敏感性对应于传统密码的混乱扩散特性。结合这些特性,提出抵抗泄露攻击的无线传感器网络分组加密算法。基于混沌S盒方法完成分组初加密,生成子密钥,构建抵抗泄漏攻击的CCA安全密钥以优化无线传感器网络分组加密,通过算法输入的方式优化密钥的加密算法,定义封装密钥空间。利用CPA密钥的安全性保证加密密钥输出,满足无线传感器网络抵抗泄漏攻击的要求。仿真结果表明:所提方法的信息熵值始终高于7.99,执行时间始终低于12.1 ms,所需存储空间始终低于126 bytes,保密性能和保密效果更好,具有较高的实际应用价值。

一维鲁棒混沌映射及S盒的设计

本文利用Li-York混沌判别定理,构造了一类分段线性连续混沌映射.基于此类映射,建立了一个构造一类分段非线性鲁棒混沌映射的判别定理.作为应用,构造了一个由多项式函数和三角函数映射合成的分段非线性鲁棒混沌映射.通过计算该混沌映射的分岔图,验证了映射在参数范围内的混沌性.作为鲁棒混沌的应用,设计了三个基于分段非线性鲁棒混沌映射的伪随机数发生器.在此基础上,利用混沌映射对初始参数的敏感性,提出了批量生成S盒的算法.S盒密码性能的分析结果表明,生成的S盒具有良好的密码学性能,可以较好的抵抗线性与差分攻击,为密码算法的研究发展提供基础与条件.

考虑励磁顶值与PSS的混沌和分岔现象

电力系统中的混沌对传统的稳定分析和安全控制而言 ,是一个巨大的挑战。文中研究了发电机励磁顶值和 PSS回路对电力系统的振荡失稳和混沌现象的影响。研究表明 ,当计及励磁顶值极限时 ,或在 PSS参数配置合理情况下 ,可能导致系统 Hopf分岔 (HB)现象不出现或 HB点与鞍—节分岔 (SNB)点十分接近。由于在小扰动稳定框架下 ,HB出现是混沌产生的前提 ,HB不能出现时 ,混沌现象也将消失。合理配置 PSS参数 ,可为系统提供正阻尼 ,从而能够显著抑制 HB及混沌现象的产生。

S波段雷达实测海杂波混沌分形特性分析

S波段海杂波信号表现了非线性和频谱时变性,传统的谱分析方法,无法反映该信号在时间上的演化规律。该文首先引入分形布朗运动模型,基于S波段雷达实测海杂波数据,计算了该分形模型的海杂波Hurst指数,进而求得了其分形维数。然后利用经典的Rosenstein方法,计算了S波段实测海杂波的最大Lyapunov指数,从而证实了S波段雷达海洋回波信号具有混沌分形特性。最后进行了计算机实验,验证了本文的结论。该文的工作为S波段海洋雷达的目标探测提供了一种新的途径。

电网混沌系统的T-S模糊非线性PI控制

为抑制电网的混沌现象,提出了一种电网混沌系统的T-S模糊模型的非线性状态比例-积分(PI)控制方法。通过建立电网混沌系统的T-S模糊模型,将具有强非线性的电力系统分解为局部线性化的子系统,针对每一个子系统设计非线性状态比例-积分控制器,理论论证了控制系统的稳定性。最后由仿真实验证实了该方法能够有效抑制电网的混沌现象。

应用T-S模糊方法对铁磁谐振过电压的混沌抑制

抑制和控制铁磁谐振过电压对实现智能电网中重要的"自愈"功能具有重要的意义。为此,运用非线性动力学理论于抑制中性点接地系统所发生的具有混沌效应的铁磁谐振。通过分析铁磁谐振电路所表现出的混沌特性,并针对电力系统中参数无法完全已知的限制,首次提出建立谐振系统的T-S模糊模型,制定合适的模糊规则,并应用平行分布补偿法设计模糊控制器来抑制铁磁谐振过电压,以达到迅速控制的良好效果。另外,通过Lya-punov理论验证了该控制器符合系统稳定性要求。仿真结果也验证了该方法的有效性,同时克服了传统方法对参数完全精确已知的限制。

基于参数识别应用Backstepping design控制Lü′s混沌吸引子

混沌控制在最近十几年的研究中已经取得了长足的进展,形成了许多比较成熟而且有效的控制技术和方法,如:OGY控制、线性状态空间反馈等 但对于带有未知参数的系统,前面提到的方法常常无法达到预期的控制 通过构造识别函数识别L櫣′s混沌系统的未知参数,然后应用Backsteppingdesign控制L櫣′s混沌吸引子,将L櫣′s混沌吸引子控制到一个稳定的周期轨道。