耦合哈密顿系统中测度同步发生机理的研究

测度同步是在耦合哈密顿系统中发现的一种奇特现象.采用Poincaré截面方法,研究了离散及连续的哈密顿系统中测度同步的发生机理.结果表明,测度同步的发生源于相空间分界线的穿越行为.     

利用白噪声实现混沌系统线性广义同步的研究

给定一个混沌驱动系统和同步函数，通过服从白噪声分布的单向耦合，构造出混沌响应系统，使之与驱动系统达到线性广义同步化.研究发现，利用满足一定条件的白噪声可以实现驱动-响应系统的线性广义同步.以Chua电路为例进行了数值仿真，其结果与理论计算相一致. 关键词： 混沌系统 广义同步 白噪声     

耦合映射混沌同步系统在加性噪声中的筛形域性态

由于实际系统中噪声不可避免，噪声使得同步混沌吸引子A变成具有一定生存时间<τ>的准稳态吸引子A′.以加性噪声作用下的二维耦合映射混沌同步系统为例，给定系统实验时间长 度T，解析发现：仅当<τ>>2T时准稳态同步混沌吸引子的筛形吸引域才可被定性观察到；而 当<τ><2T时则不复存在，此时，根据原无噪声时的筛形吸引域特征的不同，筛形域不仅可 以转变成时变筛形结构，还可以转变成分形结构.同时利用数值模拟作了进一步验证.该结果 对于二维耦合映射混沌同步系统具有普遍意义. 关键词： 混沌同步 筛形吸引域 瞬态混沌 耦合映射 加性噪声     

一种基于非完整二维相空间分量置换的混沌检测方法

由于混沌时间序列和随机过程具有很多类似的性质, 因而在实际中很难将两者区分开来. 混沌信号检测与识别是混沌时间序列分析中一个重要的课题. 混沌信号是由确定性的混沌映射或混沌系统产生的, 相比于高斯白噪声序列, 其在非完整的二维相空间中表现出更加丰富的结构特性. 本文通过研究混沌时间序列和高斯白噪声序列在非完整二维相空间中的分布特性, 利用混沌信号的非线性动力学特性, 提出了一种基于非完整二维相空间分量置换的混沌信号检测方法. 该方法首先由接收序列得到非完整的二维相空间, 基于第一维分量大小关系实现对第二维分量的置换与分组, 进一步求得F检验统计量. 然后利用混沌系统的局部特性, 获取非完整二维相空间的动力学结构信息, 实现对混沌序列的有效检测. 在高斯白噪声条件下对多种混沌信号进行了信号检测的数值仿真. 仿真结果表明: 相比置换熵检测, 本文所提算法所需数据量小、计算简单以及具有更低的时间复杂度, 同时对噪声具有更好的鲁棒性.     

Sprott-B和Sprott-C系统之间的耦合混沌同步

Sprott-B和 Sprott-C是拓扑等价的异结构混沌系统. 利用系统变量线性耦合方法实现二系统之间的混沌同步；根据Lyapunov稳定性理论，确定了二系统达到同步时耦合系数的阈值. 设计了实现二系统耦合同步的实验电路，实验结果证明了理论分析的正确性. 基于Sprott-B和 Sprott-C异结构系统混沌同步，提出了一种新的具有更好保密性能的混沌保密通讯方法. 关键词： 线性耦合 混沌同步 异结构系统 拓扑等价     

干扰信号对两种混沌加密系统的影响及分析

通过加入高斯白噪声干扰，对Lorenz和Liu两种混沌加密系统进行噪声干扰的分析和计算.结果表明：Liu混沌系统抗噪声干扰能力好于Lorenz混沌系统，连续信源的抗干扰能力好于离散信源的抗干扰能力. 关键词： Lorenz系统 Liu系统 抗干扰性 信噪比     

连续时间混沌系统的自适应Ｈ∞ 同步方法

提出了一种连续时间混沌系统的自适应H∞同步方法.当响应系统没有受噪声干扰影 响时，所设计的自适应H∞同步控制器能够使响应系统与驱动系统全局同步.当响应 系统受噪声干扰影响时，自适应H∞同步控制器能够使噪声干扰对同步误差的影响小于期望的水平.最后，以蔡氏电路混沌系统为例来说明所提方法的有效性. 关键词： 混沌 混沌同步 自适应控制 H∞控制 自适应H∞同步     

统一混沌系统的耦合同步

对线性耦合的两个统一混沌系统同步进行研究.基于线性时变连续系统的稳定性理论，得到初始值不同的两个统一混沌系统全局渐进同步的一种新的充分条件.另外，与已经提出的判定统一混沌系统同步的方法进行比较，发现这里得到的充分条件的约束关系少、缺少保守性，而且满足的耦合系数范围更广.将该方法应用于统一混沌系统，数值仿真表明了该法的有效性与可行性. 关键词： 统一混沌系统 耦合同步 线性时变连续系统     

声光双稳系统的混沌同步

首先给出布拉格型声光双稳系统耦合驱动的混沌同步化方案，用最大条件Ｌｙａｐｕｎｏｖ指数分析方法得出耦合驱动下系统混沌输出同步化条件，发现通过适当比例的耦合驱动可以使两组混沌系统达到同步的混沌输出。分析此混沌同步化方案可以抵抗噪声的干扰，并且在两系统出现偏差时仍可以实现混沌同步，找到了实用的单变量延时微分系统非Ｐｅｃｏｒａ－Ｃａｒｒｏｌｌ规则的混沌同步化方案。最后做了实验验证。     

布拉格声光双稳系统时空混沌的单向耦合同步

使用非线性动力学中的一维和二维耦合格子模型研究两个声光双稳系统的时空混沌同步.将驱动系统的输出以适当的比例耦合到响应系统并进行均衡, 能实现两系统的时空混沌同步.利用计算最大条件Lyapunov指数, 给出达到同步所需的最小耦合强度与系统参数的关系. 数值实验表明,在小噪声影响时仍然可以实现两系统的同步, 此法具有一定的抗干扰能力. 关键词： 单向耦合同步 时空混沌 布拉格声光双稳系统     

Synchronization rate of synchronized coupled systems

Synchronization phenomena, an emergent property in networks of interacting dynamical elements, are widely observed in nature, and have become the subject of intense research. Here we will investigate the synchronization rate problem in coupled limit-cycle and chaotic oscillators. Based on the mode decomposition method and Gershgörin's discs theorem, some sufficient conditions for synchronization of coupled systems are obtained, and a synchronization rate is then derived. Such a synchronization rate indicates that the error functions between state variables of underlying individual systems tend to zero in the exponential form as time tends to the infinity. Several numerical examples are also given to validate the theoretical results.     

Experimental investigation of high-quality synchronization of coupled oscillators

We describe two experiments in which we investigate the synchronization of coupled periodic oscillators. Each experimental system consists of two identical coupled electronic periodic oscillators that display bursts of desynchronization events similar to those observed previously in coupled chaotic systems. We measure the degree of synchronization as a function of coupling strength. In the first experiment, high-quality synchronization is achieved for all coupling strengths above a critical value. In the second experiment, no high-quality synchronization is observed. We compare our results to the predictions of the several proposed criteria for synchronization. We find that none of the criteria accurately predict the range of coupling strengths over which high-quality synchronization is observed. (c) 2000 American Institute of Physics.     

耦合分数阶混沌振荡器的主-从同步

近年来对分数阶系统的动力学研究得到了较为广泛的关注。本文研究了基于主-从耦合同步法的同步技术并实现了两个耦合的分数阶振荡器的混沌同步。仿真结果表明：在适当的耦合强度的调节下，该方法可实现两个耦合分数阶混沌振荡器的准确同步，且分数阶混沌振荡器的同步率明显慢于整数阶混沌振荡器的同步率；而耦合分数阶混沌振荡器在实现同步的过程中，随着阶数的提高，同步误差曲线变得平滑，这表明，系统阶数的提高改善了耦合混沌振荡器实现同步的平稳性。     

An approach to chaotic synchronization

This paper deals with the chaotic oscillator synchronization. An approach to the synchronization of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. It has been shown that complete synchronization, phase synchronization, lag synchronization, and generalized synchronization are the particular cases of the synchronized behavior called "time-scale synchronization." The quantitative measure of chaotic oscillator synchronous behavior has been proposed. This approach has been applied for the coupled R?ssler systems and two coupled Chua's circuits.     

Synchronization of chaotic oscillator time scales

We consider chaotic oscillator synchronization and propose a new approach for detecting the synchronized behavior of chaotic oscillators. This approach is based on analysis of different time scales in the time series generated by coupled chaotic oscillators. We show that complete synchronization, phase synchronization, lag synchronization, and generalized synchronization are particular cases of the synchronized behavior called time-scale synchronization. A quantitative measure of chaotic oscillator synchronous behavior is proposed. This approach is applied to coupled Rössler systems.     

Synchronization on coupled dynamical networks

In this paper, partial synchronization (PaS) in networks of coupled chaotic oscillator systems and synchronization in sparsely coupled spatiotemporal systems are explored. For the PaS, we reveal that the existence of PaS patterns depends on the symmetry property of the network topology, while the emergence of the PaS pattern depends crucially on the stability of the corresponding solution. An analytical criterion in judging the stability of PaS state on a given network are proposed in terms of a comparison between the Lyapunov exponent spectrum of the PaS manifold and that of the transversal manifold. The competition and selections of the PaS patterns induced by the presence of multiple topological symmetries of the network are studied in terms of the criterion. The phase diagram in distinguishing the synchronous and the asynchronous states is given. The criterion in judging PaS is further applied to the study of synchronization of two sparsely coupled spatiotemporal chaotic systems. Different synchronization regimes are distinguished. The present study reveals the intrinsic collective bifurcation of coupled dynamical systems prior to the emergence of global synchronization.     

耦合不连续系统同步转换过程中的多吸引子共存

本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程.     

Analysis of phase synchronization of chaotic oscillations in terms of symbolic CTQ-analysis

The application of symbolic CTQ-analysis for studying synchronization of chaotic oscillations is considered. This approach differs substantially from its analogs since it makes it possible to diagnose and measure quantitatively the characteristics of intermittency regimes in synchronization of chaotic systems and, hence, to analyzer the temporal structure of synchronization. The application of the symbolic analysis apparatus based on the T alphabet to systems with phase locking and synchronization of time scales is demonstrated for the first time. As an example, a complex system of two mutually coupled nonidentical Rössler oscillators in the helical chaos regime with attractors having an ill-conditioned phase is considered. The results show that the method considered here makes it possible to reliably diagnose synchronism sooner than a phase locking and/or time-scale synchronization threshold is detected.     

Stages of chaotic synchronization

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.     

INVERSE SYNCHRONIZATION OF CHAOTIC SYSTEMS IN AN ERBIUM-DOPED FIBRE DUAL-RING LASER USING THE MUTUAL COUPLING METHOD

Inverse synchronization of chaos is a type of synchronization in which the dynamical variables of two chaotic systems are inversely equal. In this paper, we present a scheme for inverse synchronization of two chaotic systems in an erbium-doped fibre dual-ring laser using the mutual coupling method. For realistic values of the systems, we demonstrate two kinds of results, as follows. (1) Two independent identical chaotic systems can go into inversely synchronized chaotic oscillation for coupling greater than 0.03. (2) When some parameter of one system varies, the state of the coupled systems could go into some periodic states directly or by inverse bifurcation. Simultaneously, they will lose the synchronization as the parameter changes.