条件Lyapunov指数和时间τ-条件Lyapunov指数的研究

本文研究条件Ｌｙａｐｕｎｏｖ指数与τ指数的定义、求解技术及其应用。两种指数从不同角度对系统本质特性进行刻划,条件Ｌｙａｐｕｎｏｖ指数在混沌同步中有重要应用,近来它还衩用来进行相空间重构问题的研究。时间τ－条件Ｌｙａｐｕｎｏｖ指数是一类利用状态变量的离散采样作驱动信号的脉冲方式的重要定量指标。本文提出一种简便的求解技术,在Ｗｏｌｆ求解Ｌｙａｐｕｎｏｖ指数谱程序的基础上,稍加改动即可使其适用于Ｌｙａｐ     

Secure Communication via Synchronization of Lur’e Systems Using Sampled-Data Controller

In this paper, synchronization of chaotic Lur’e systems using sampled-data control is applied to the secure communication problem. The message is transmitted and masked by the techniques of n-cipher and a public key obtained by the chaotic Lur’e system. The decryption of the transmitted encrypted message to recover the original message at the receiver can be achieved by synchronizing the transmitter and receiver chaotic systems. Sampled-data feedback control is used for synchronization, and a sufficient condition for obtaining feedback gain is derived in terms of linear matrix inequalities using a discontinuous Lyapunov functional. The secure communication system is simulated via Matlab along with the Chua system to show the effectiveness of the proposed result.     

噪声引导混沌同步的同步时间分析

以Logistic映射为物理模型,计算了噪声混沌系统的Lyapunov指数谱,并利用其分析了噪卢分布区间与同步时间的关系．发现同步时间与噪声分布区间内的平均Lyapunov指数直接相关．若陔区间的平均Lyapunov指数越小,则同步时间越短。最后,提出了一种基于统计分析的时间阈值估算方法．并用该方法估算了Logistic系统在不同同步精度下的时间阈值。     

一个超混沌系统及其投影同步

 通过在Lorenz系统中加入两个控制器构造出一个五维超混沌系统,系统的超混沌特性通过Lyapunov指数得到验证,对系统的平衡点和耗散性进行了分析.基于线性系统的稳定性准则,利用线性分离方法实现了该超混沌系统的投影同步.     

简并光学参量振荡器的同步研究

通过计算简并光学参量振荡器系统的李雅普诺夫指数,证明了该系统存在混沌和超混沌吸引子,即简并光学参量振荡器是混沌系统,并得到了系统处于混沌状态时的参数取值范围.进一步,利用反馈技术实现了简并光学参量振荡器的混沌同步和周期同步,给出了反馈控制的具体形式并进行了仿真计算,理论结果与数值仿真结果一致.     

Contraction Theory and Master Stability Function: Linking Two Approaches to Study Synchronization of Complex Networks

In this brief, the contraction theory is applied to the synchronization of a network. The association between the contraction principle, the Lyapunov exponents of a system, and the master stability function of the network is pointed out. Novel sufficient criteria for the fulfillment of a synchronous state are derived.      

一类混沌电路的跃变参数识别与同步*

基于李亚普诺夫稳定性理论和矩阵理论,用两种方法对一类混沌电路系统参数发生跃变情况下的参数识别与同步控制进行了理论分析和数值计算机模拟。第一种方法是通过负反馈将系统镇定到某个稳定态来识别系统的跃变参数（系统参数突然发生阶跃性变化）,通过计算李亚普诺夫指数获得反馈系数临界值。第二种方法是基于李亚普诺夫稳定性理论得到的参数观测器包含了可调节的增益系数,当两个混沌系统达到完全同步时驱动系统的5个未知参数在阶跃变化情况下也可以被准确识别。最后对两种方法的优缺点进行了比较和分析。     

Reference Symbol Assisted Multi-Stage Successive Interference Cancellation for CDMA Wireless Communication: Robustness to Parameter Imperfections with Biphase and Quadriphase spreading

This paper investigates the sensitivity to system imperfections of a reference symbol assisted multi-stage successive interference cancelling (RAMSIC) receiver. Reverse link of a CDMA system with binary antipodal modulation and coherent detection is considered. Performance of systems using either biphase and quadriphase spreading is compared under different operating conditions. Analysis of a conventional matched filter receiver operating on an AWGN channel reveals that when the number of users is small (such that the multiple access interference cannot be accurately modelled as Gaussian), quadriphase spreading has a significant advantage over biphase spreading. This advantage, however, disappears when the number of users per sector is large (of the order necessary for the multiple access interference to be considered Gaussian). Results for the RAMSIC receiver with quadriphase spreading, on the other hand, show that for hexagonal cell geometry with path loss exponent of 4 and without any forward error correction coding, the traffic capacity is between 1.17 and 1.67 times that of the IS-95. These numbers represent a significant increase over those obtained with biphase spreading. Further investigation with nonidealized cell geometries and other path loss exponents also shows substantial capacity improvement over that of conventional correlator receivers. Performance losses due to nonideal transmitter power amplifier gating, imperfect power control and synchronization errors in the RAKE receiver are also determined. The results for biphase spreading show that for path loss exponent of 4, imperfect amplifier gating causes relatively minor decrease in the traffic capacity, while no such effect is observed for path loss exponents of 2 and 3. As expected, relaxing of power control for both biphase and quadriphase spreading has a similar capacity reducing effect. In spite of these two effects the resultant capacity is still significantly higher than that with the conventional matched filter receiver. Capacity increase with quadriphase over biphase spreading is between 1.4 and 2.0 times. Chip synchronization errors of the order to be expected in a properly designed conventional CDMA system have only minimal effect on performance. Therefore, we conclude that conventional synchronization algorithms should perform adequately with successive interference cancelling receivers considered in the paper.     

Three-Dimensional Chaotic Autonomous System with a Circular Equilibrium: Analysis,Circuit Implementation and Its Fractional-Order Form

A three-dimensional autonomous chaotic system with a circular equilibrium is investigated in this paper. Some dynamical properties and behaviors of this system are described in terms of equilibria, eigenvalue structures, bifurcation diagrams, Lyapunov exponents, time series and phase portraits. For specific parameters, the system displays periodic and chaotic attractors. The physical existence of the chaotic behavior found in the proposed system is verified by using the Orcad-PSpice software and experimental verification. A good qualitative agreement is shown between the experimental results, PSpice and numerical simulations. Furthermore, the commensurate fractional-order version of the system with a circular equilibrium is numerically studied. It is found that chaos exists in this system with order less than three. By tuning the commensurate fractional order, the system with a circular equilibrium displays chaotic and periodic attractors, respectively. Finally, chaos synchronization of identical fractional-order chaotic systems with a circular equilibrium is achieved by using the unidirectional linear error feedback coupling. It is shown that the fractional-order chaotic system can achieve synchronization for appropriate coupling strength.     

离散动力系统无退化-配置N个正Lyapunov指数

针对离散时间混沌动力学系统,该文提出一种基于矩阵特征值以及特征向量配置Lyapunov指数为正的新算法。计算离散受控矩阵的特征值以及特征向量,设计一类具有正Lyapunov指数的通用控制器,理论证明系统轨道的有界性和Lyapunov指数的有限性。对线性反馈算子以及微扰反馈算子进行数值仿真分析,验证了算法的正确性、通用性和有效性。性能评估表明,与Chen-Lai算法相比,该方法可以构建较低计算复杂度的混沌系统,并且运行时间较短,其输出序列也具有较强的随机性,实现了无退化、无兼并的离散混沌系统。     

双区半导体激光器的超混沌及同步

基于双区半导体激光器的速率方程,研究了双区半导体激光器的超混沌现象,给出了双区半导体激光器产生超混沌的条件;利用驱动-响应法实现了双区半导体激光器的超混沌同步,通过计算激光系统最大条件李亚谱诺夫指数随注入强度的变化,得到实现超混沌同步的注入参量的取值范围.     

Global synchronization and asymptotic stability of complex dynamical networks

Global synchronization and asymptotic stability of complex dynamical networks are investigated in this paper. Based on a reference state, a sufficient condition for global synchronization and stability is derived. Unlike other approaches where only local results were obtained, the complex network is not linearized in this paper. Instead, the sufficient condition for the global synchronization and asymptotical stability is obtained here by introducing a reference state with the Lyapunov stability theorem rather than the Lyapunov exponents, and this condition is simply given in terms of the network coupling matrix therefore is very convenient to use. Furthermore, the developed technique is applied to networks consisting of nodes with unknown but bounded nonlinear functions. A typical example of a complex network with chaotic nodes is finally used to verify the theoretical results and the effectiveness of the proposed synchronization scheme.     

用李雅谱诺夫指数配置法控制统一混沌系统

解析设计控制器，通过配置相应的李雅谱诺夫指数，使统一混沌系统趋于预期点．由于受控后系统李雅谱诺夫指数具有先知性，因此，我们可以根据需要改变李雅谱诺夫指数的大小来控制系统收敛速度．设计还表明，受控的统一混沌系统的收敛情况与参数无关。     

Design of a tensile-type 3-D multi-scroll chaotic system and its application in secure communication

A kind of tensile-type 3-D multi-scroll chaotic attractor based on Chua's circuit was successfully designed. The chaos generation mechanism was studied by analyzing the symmetry and invariance, the existence of the dissipation, as well as the system equilibrium and stability. Then, some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic dynamical behaviors of the new chaotic system were introduced, either numerically or analytically. At the same time, the chaotic circuit of this system was realized by PSPICE. Finally, based on Lyapunov theorem and unidi-rectionally coupled method, the synchronization of the chaotic system has also been investigated. With this approach, the novel system can be applied to secure communication, which can achieve the purpose of covering specific signals. The experimental results are in agreement with numerical simulation results, which verifies the availability and feasibility of this method.     

一类四维超混沌系统的同步研究

采用误差变量的线性组合对一类四维动态超混沌系统进行单向反馈控制，解析地证明了实现同步的可能性，从Lyapunov理论角度分析了对于四维动态系统采用单变量单向耦合的可行性，求出同步所需控制器要满足的条件。当驱动系统参数做周期变化时，用文中的控制器实现了两个超混沌系统很好同步。     

一种混沌系统的控制方法

系统的李雅普诺夫指数可用作判断系统是否混沌的依据，通过改变系统李雅普诺夫指数改变系统的运动状态，达到控制混沌系统的目的，理论分析和仿真实验结果均表明，该控制策略是有效的，可以实现系统的快速稳定。     

简化Lorenz混沌系统的投影同步控制

针对最新研究的简化Lorenz混沌系统模型,分别采用比例投影同步和广义函数投影同步控制策略,研究了两个不同初值的简化Lorenz混沌系统的同步问题.基于罗斯-霍尔维兹准则和Lyapunov稳定性原理,推导了实现两混沌系统投影同步的同步定理,确定了实现投影同步的控制参数的取值范围:分析了控制参数对同步系统性能的影响规律....     

受激喇曼散射系统构成星型网络的耦合混沌同步

提出了一种实现星型单向激光网络耦合的混沌同步方法。通过适当分离配置各系统的线性项,将其余项作为各节点间的相互耦合函数,研究以四个受激拉曼散射系统构成星型单向激光网络的同步方法。基于Lyapunov定理,构造适当的Lyapunov函数从而实现复杂网络的完全同步。进一步仿真模拟验证了理论分析结果的正确性。     

基于线性状态反馈方法的Nadolschi混沌系统同步

研究了一类新型混沌系统——Nadolschi系统的同步控制问题。首先为响应系统设计一个多变量线性状态反馈控制器,进而将Nadolschi系统的同步控制问题转化为误差系统零平衡点的镇定问题。然后,根据Lyapunov稳定性理论,得出使Nadolschi混沌系统达到渐近同步的充分条件。仿真结果验证了所提方法的有效性,所设计的控制器具用结构简单,易于实现等优点。     

半导体激光器的混沌驱动同步

利用混沌驱动同步法研究了在电流调制下的半导体激光器的混沌同步。首先数值计算了系统最大Lyapunov指数随调制强度的变化情况,确定了激光器处于混沌态的参数区间。然后分别实现了同地激光器系统和异地激光器系统的混沌驱动同步。响应激光器间相关系数的数值计算表明,两种激光器系统均能达到很好的混沌同步。以三个响应激光器为例,将响应系统推广到多个激光器,并且实现了两种激光器系统的混沌同步。