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1.
We propose a definition of the discrete Lyapunov exponent for an arbitrary permutation of a finite lattice. For discrete-time dynamical systems, it measures the local (between neighboring points) average spreading of the system. We justify our definition by proving that, for large classes of chaotic maps, the corresponding discrete Lyapunov exponent approaches the largest Lyapunov exponent of a chaotic map when M/spl rarr//spl infin/, where M is the cardinality of the discrete phase space. In analogy with continuous systems, we say the system has discrete chaos if its discrete Lyapunov exponent tends to a positive number, when M/spl rarr//spl infin/. We present several examples to illustrate the concepts being introduced.  相似文献   

2.
Integrated Circuits of Map Chaos Generators   总被引:1,自引:0,他引:1  
A chaotic noise is one of the most important implements for information processing such as neural networks. It has been suggested that chaotic neural networks have high performance ability for information processing. In this paper, we report two designs of a compact chaotic noise generator for large integration circuits using CMOS technology. The chaotic noise is generated using map chaos. We design both of the logistic map type and the tent map type circuits. These chaotic noise generators are compact as compared with the other circuits. The results show that the successful chaotic operations of the circuits because of the positive Lyapunov number. We calculate the Lyapunov exponents to certify the results of the chaotic operations. However, it is hard to estimate its accurate number for noisy data using the conventional method. And hence, we propose the modified calculation of the Lyapunov exponent for noisy data. These two circuits are expected to be utilized for various applications.  相似文献   

3.
Signals arising out of nonlinear dynamics are compelling models for a wide range of both natural and man-made phenomena. In contrast to signals arising out of linear dynamics, extremely rich behavior is obtained even when we restrict our attention to one-dimensional (1-D) chaotic systems with certain smoothness constraints. An important class of such systems are the so-called Markov maps. We develop several properties of signals obtained from Markov maps and present analytical techniques for computing a broad class of their statistics in closed form. These statistics include, for example, correlations of arbitrary order and all moments of such signals. Among several results, we demonstrate that all Markov maps produce signals with rational spectra, and we can therefore view the associated signals as “chaotic ARMA processes,” with “chaotic white noise” as a special case. Finally, we also demonstrate how Markov maps can be used to approximate to arbitrary accuracy the statistics any of a broad class of non-Markov chaotic maps  相似文献   

4.
Chaos control on universal learning networks   总被引:2,自引:0,他引:2  
A new chaos control method is proposed which is useful for taking advantage of chaos and avoiding it. The proposed method is based on the following facts: (1) chaotic phenomena can be generated and eliminated by controlling the maximum Lyapunov exponent of the systems, and (2) the maximum Lyapunov exponent can be formulated and calculated by using higher-order derivatives of universal learning networks (ULNs). ULNs consist of a number of interconnected nodes which may have any continuously differentiable nonlinear functions in them and where each pair of nodes can be connected by multiple branches with arbitrary time delays. A generalized learning algorithm has been derived for the ULNs in which both first-order derivatives (gradients) and higher-order derivatives are incorporated. In simulations, parameters of ULNs with bounded node outputs were adjusted for the maximum Lyapunov exponent to approach the target value, and it has been shown that a fully-connected ULN with three sigmoidal function nodes is able to generate and eliminate chaotic behaviors by adjusting these parameters  相似文献   

5.
该文基于混沌理论提出了一种使用海量网络流量数据对大规模网络性能进行有效评估的方法。在长期链路利用率数据呈现出明显的周期性行为,和短期链路利用率数据具有混沌特征的前提下,选取最大Lyapunov指数作为一项性能评估参数来评估网络性能。分析结果表明最大Lyapunov指数较常见统计量如数学期望、方差等更能有效反映流量的行为趋势。  相似文献   

6.
研究了实际采集的海杂波的关联维及最大Lyapunov指数。结果表明,海杂波具有混沌特性。基于复杂非线性系统的相空间重构理论和混沌信号可短期预测的特征,提出了强海杂波中的微弱目标信号检测的神经网络方法,给出了雷达检测的模型。  相似文献   

7.
一个新的混沌模型及其硬件实现   总被引:1,自引:1,他引:0  
该文提出了一个新的非线性动力学系统模型并对其进行了仿真研究,结果表明此模型具有正的李雅普诺夫指数,表现出时域伪随机性和连续的频谱,因而此模型是一个混沌发生器。由于它的线性子系统的条件李雅普诺夫指数均为负,因而是可同步子系统,能够用于混沌保密通信。该文还给出了此模型的两种分段线性电路实现方法。  相似文献   

8.
9.
通过对一个注入激光系统的分岔图、李雅普诺夫(Lyapunov)指数谱、功率谱和相轨道的数值计算与分析,得到了系统出现不动点、极限环、混沌、超混沌的参数区间。为进一步研究该系统在混沌和起混沌状态下的统计性质奠定了基础。  相似文献   

10.

该文以通信系统中常用的典型微波部件——同轴连接器为研究对象,基于混沌理论对获得的同轴连接器的无源互调(PIM)功率时间序列进行分析,验证了使用混沌理论预测无源互调的有效性。首先通过实验系统获得同轴连接器的3阶无源互调功率时间序列,并对得到的实验数据进行相空间重构,确定该时间序列的最佳嵌入维数m和延迟时间τ。然后,结合最佳嵌入维数和延迟时间,分别构建相图和使用小数据量法计算该时间序列的最大Lyapunov指数,从而从定性和定量角度验证了该无源互调功率时间序列具有混沌特性。在此基础上,基于获得的最大Lyapunov指数对该无源互调功率时间序列进行混沌预测,在最大可预测尺度范围内,理论预测值与实验值最大误差为2.61%,表明采用混沌方法预测无源互调功率效果较好。该文提出的使用混沌理论预测通信系统中微波部件无源互调功率的方法,为开展无源互调抑制技术研究,提高通信系统的性能提供了新思路。

  相似文献   

11.
超声键合换能系统中劈刀的振动特性分析   总被引:1,自引:0,他引:1  
阐述了Lyapunov指数作为振动信号的混沌判断原理,并对换能系统的振动信号进行分析与研究,计算了换能系统在不同加载压力下劈刀的振动时间序列的Lyapunov指数.结果表明振动信号中的最大Lyapunov指数均大于0,根据混沌理论可以判定换能系统振动信号中存在混沌现象,应该采用混沌的方法研究与分析换能系统振动信号.通过不同加载压力下的振动速度信号的RMS值与最大Lyapunov指数的比较,发现两者随压力变化趋势相同,为进一步研究超声引线键合换能系统的振动特性提供了有价值的参考.  相似文献   

12.
混沌研究方法在雷达海杂波分析中的应用   总被引:4,自引:0,他引:4  
本文讨论了混沌信号的基本特性,相空间重构,Lyapunov指数,关联维、功率谱指数等用于表征未知动态系的混沌中的重要概念,并将它们应用于来自海洋表面雷达后向散射海杂波信号的分析中。通过对海杂波的分析,计算得出:海杂波有有限的关联维和正的Lyapunov指数,功率谱指数呈指数下降。这说明海杂波具有混沌特性。  相似文献   

13.
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。  相似文献   

14.
李钢 《激光杂志》2007,28(3):27-28
分析了单模激光Lorenz系统和新系统的动力学特性.基于非线性反馈控制器的设计,利用跟踪控制使处于混沌和超混沌的两系统之间的拓扑不等价的异结构混沌系统成功地达到了混沌同步,依据线性稳定性理论分析,确定了控制系统的稳定性.数值模拟表明,通过适当地选择反馈增益系数,响应系统得到了有效控制.由于控制过程中无需计算Lyapunov指数,异结构混沌系统间的拓扑结构亦可以有较大差异,可降低混沌控制工作量和提高保密通信的性能.  相似文献   

15.
针对微弱信号幅值很小,常被噪声淹没,而传统去噪方法效果并不理想,研究基于混沌与高阶累积量的微弱正弦信号检测方法,建立仿真模型,并将最大李雅普诺夫Lyapunov指数作为判断混沌系统相变的量化依据.自动识别混沌系统的临界状态,从而准确确定系统的策动力临界闽值。仿真实验表明该方法能有效检测出淹没在高斯噪声中的微弱正弦信号,检测信噪比为-37dB时,幅度检测相对误差为1.9%。该方法幅度检测门限低,具有广泛应用前景。  相似文献   

16.
一种混沌网络简单电路实现   总被引:2,自引:0,他引:2  
本文利用简单的非线性电子元件设计成混沌电路,该电路具有设计简单,易于集成等特点。利用多控制参数使得该混沌电路具有丰富的混沌动力学行为,本文利用Lyapunov指数,从理论上分析控制参数对电路输出的影响。根据理论分析结果,调节电路的参数,可以成功地看到不动点、倍周期、混沌现象。这一简单电路可望在混沌神经网络,混沌通讯领域获得应用。  相似文献   

17.
武薇  夏敏磊  庞全  范影乐   《电子器件》2007,30(4):1384-1386
研究了相同结构的混沌系统耦合后所得到的新系统的时空动力学行为及其系统特性.通过计算机仿真得到了耦合系统的分岔图和Lyapunov指数;在系统初值受噪声干扰的情况下,对混沌轨道偏移的均方根误差值与参与耦合的混沌子系统数量之间的关系进行了研究.计算机仿真结果证明,耦合后得到的新系统仍然是混沌态的,因此,它依旧保持了对初值的敏感性;但同时降低了混沌轨道指数漂移的不稳定性,在一定程度上抑制了噪声对系统初值的干扰.  相似文献   

18.
采用改变系统乘积项的方法,在已提出的混沌系统的基础上,构建了一个切换混沌系统。分析了平衡点的性质,混沌吸引子相图和Lyapunov指数等特性,设计了可实现切换混沌系统的电路并进行了电路实验,实现结果与仿真结果一致:  相似文献   

19.
Characterizing chaos through Lyapunov metrics   总被引:1,自引:0,他引:1  
Science, engineering, medicine, biology, and many other areas deal with signals acquired in the form of time series from different dynamical systems for the purpose of analysis, diagnosis, and control of the systems. The signals are often mixed with noise. Separating the noise from the signal may be very difficult if both the signal and the noise are broadband. The problem becomes inherently difficult when the signal is chaotic because its power spectrum is indistinguishable from broadband noise. This paper describes how to measure and analyze chaos using Lyapunov metrics. The principle of characterizing strange attractors by the divergence and folding of trajectories is studied. A practical approach to evaluating the largest local and global Lyapunov exponents by rescaling and renormalization leads to calculating the m Lyapunov exponents for m-dimensional strange attractors either modeled explicitly (analytically) or reconstructed from experimental time-series data. Several practical algorithms for calculating Lyapunov exponents are summarized. Extensions of the Lyapunov exponent approach to studying chaos are also described briefly as they are capable of dealing with the multiscale nature of chaotic signals. The extensions include the Lyapunov fractal dimension, the Kolmogorov--Sinai and Re/spl acute/nyi entropies, as well as the Re/spl acute/nyi fractal dimension spectrum and the Mandelbrot fractal singularity spectrum.  相似文献   

20.
基于混沌、分形理论的多径衰落分析   总被引:3,自引:0,他引:3  
胡刚  朱世华  谢波 《电子学报》2003,31(7):1039-1042
本文首次将混沌、分形等非线性理论引入多径衰落的研究,针对现场实测数据分析了它的非线性动力特征.首先通过重构状态空间和关联维数验证了其动力机制的有限维自由度,然后通过计算其Lyapunov指数考察了系统的时空演化特性,最后利用分形机制对多径信号进行了重构.研究结果表明,与传统的随机模型相比,非线性动力模型能更恰当地描述多径衰落的内在物理机制.  相似文献   

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