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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 相似文献
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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. 相似文献
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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 相似文献
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声光双稳系统的混沌同步 总被引:6,自引:0,他引:6
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。 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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A. E. Hramov A. A. Koronovskii Yu. I. Levin 《Journal of Experimental and Theoretical Physics》2005,100(4):784-794
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. 相似文献
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Zheng Zhi-gang Feng Xiao-qin Ao Bin Michael C. Cross 《Frontiers of Physics in China》2006,1(4):458-467
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. 相似文献
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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. 相似文献
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A. V. Makarenko 《Technical Physics》2016,61(2):265-273
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. 相似文献
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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. 相似文献
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INVERSE SYNCHRONIZATION OF CHAOTIC SYSTEMS IN AN ERBIUM-DOPED FIBRE DUAL-RING LASER USING THE MUTUAL COUPLING METHOD
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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. 相似文献