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混沌系统单变量可预报性研究 总被引:5,自引:4,他引:1
对于n维的混沌系统, 不同变量的可预报性是不同的。为了研究混沌系统中单个变量的可预报性, 本文在以前提出的混沌系统整体的非线性局部Lyapunov指数基础上(李建平等, 2006), 引入了单变量的非线性局部Lyapunov指数及其相关统计量, 进一步完善了非线性误差增长理论。通过应用到几个混沌个例, 结果表明单变量的非线性局部Lyapunov指数及其相关统计量可以用来定量地研究多维混沌系统中不同变量的可预报性, 系统不同变量的可预报性之间不是相互独立的, 而是单个变量的可预报期限与系统整体的可预报期限之比都近似保持一个常数, 但各个变量的常数值有所不同。 相似文献
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本文考虑了具有混合时变延时和不同时标的混沌忆阻竞争神经网络的自适应同步问题.使用Lyapunov泛函方法和不等式分析技术,设计了一类新的具有反馈控制律的自适应控制器以取得网络同步及指数同步目的,提出了不用过多计算,如求解线性矩阵不等式或复杂代数计算的保证网络同步条件;同时,所获条件也可以应用到已有文献里关于忆阻器网络不同数学模型中.最后,通过实例验证了本文获得的理论结果的有效和正确性. 相似文献
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误差非线性的增长理论及可预报性研究 总被引:2,自引:9,他引:2
对非线性系统的误差发展方程不作线性化近似,直接用原始的误差发展方程来研究初始误差的发展,提出了误差非线性的增长理论。首先,在相空间中定义一个非线性误差传播算子,初始误差在这个算子的作用下,可以非线性发展成任意时刻的误差;然后,在此基础上,引入了非线性局部Lyapunov指数的概念。由平均非线性局部Lyapunov指数可以得到误差平均相对增长随时间的演变情况;对于一个混沌系统,误差平均相对增长被证明将趋于一个饱和值,利用这个饱和值,混沌系统的可预报期限可以被定量地确定。误差非线性的增长理论可以应用于有限尺度大小初始扰动的可预报性研究,较误差的线性增长理论有明显的优越性。 相似文献
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利用33模Lorenz系统得到的"理想"混沌时空序列,作为时空混沌序列"发生器".通过状态空间重构,建立"场时间序列"局域近似预测模型,对资料空间分辨率,资料的长度、噪音,以及模型的参数选取等因素进行敏感性试验分析,了解时空混沌序列预测中误差产生和增长的一些影响因素.得到以下初步结论:对于理想混沌时空序列(33模Lorenz系统)而言,与系统相适应的资料空间分辨率和较长的资料长度都将会提高预测精度;可预报时效与资料长度之间近似服从指数关系.另外,在建立预测模型时,适当的邻近点数目,以及采用二阶映射关系和迭代法都可以有效地改善预测精度.对于加入噪音的混沌时间序列,通过"场时间序列"的局域近似方法和4阶自回归方法的预测试验的对比表明,前者显示了更强的抗"干扰"能力.以上结论可以有分析地应用于短期气候预测中. 相似文献
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基于NCEP/NCAR再分析资料计算出的西太平洋副高活动的三种特征指数,利用相空间重构方法对副高活动的三种特征指数的混沌特性和分数维进行了计算。计算结果表明,副高的短期活动存在混沌吸引子,副高脊线指数和面积指数动力系统的独立变量数目的上、下限分别为3和6,分析结果为副高动力系统的重构研究奠定了基础。 相似文献
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HEIFE绿洲和沙漠地区大气边界层湍流混沌特性研究 总被引:8,自引:1,他引:7
利用“黑河实验”期间张掖、沙漠观测站加强观测期间1991年6月20日09:00至1991年10月2日09:00时段内水平风速的观测资料,计算分析了有关测量混沌的特征量:关联维数。Lyapunov指数和Kolmogorow熵。 相似文献
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不同下垫面大气边界层湍流的混沌特性研究 总被引:2,自引:0,他引:2
根据3 种不同观测资料,计算和分析了有关诊断具有耗散结构的系统混沌运动的特征量:功率谱、关联维数、Lyapunov 指数和关联熵。结果表明:尽管下垫面明显不同,大气边界层湍流均为混沌运动。 相似文献
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Daily rainfall and temperature data from 47 locations across Nigeria for the 36-year period 1979–2014 were treated to time series analysis technique to investigate some nonlinear trends in rainfall and temperature data. Some quantifiers such as Lyapunov exponents, correlation dimension, and entropy were obtained for the various locations. Positive Lyapunov exponents were obtained for the time series of mean daily rainfall for all locations in the southern part of Nigeria while negative Lyapunov exponents were obtained for all locations in the Northern part of Nigeria. The mean daily temperature had positive Lyapunov exponent values (0.35–1.6) for all the locations. Attempts were made in reconstructing the phase space of time series of rainfall and temperature. 相似文献
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In this paper, the attractors of turbulent flows in phase space are reconstructed by the time delay technique using observed data of atmospheric boundary-layer turbulence, which include high resolution temperature, humidity andthree-dimensional wind speed measurements in Gansu province and Beijing, China. The correlation dimensions and largest Lyapunov exponents have been computed. The results indicate that all the largest Lyapunov exponents in different conditions of time, site and atmospheric stability are greater than zero. This means that the atmospheric boundary-layer turbulence system is really chaotic and has appropriate low-dimensional strange attractors whose dimension numbers range from 3 to 7 and vary with different variables (dynamical variables or non-dynamical variables) and atmospheric stability. Turbulent kinetic energy is first applied to reconstruct the attractor of turbulence, and is found to be feasible. 相似文献
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Since the last International Union of Geodesy and Geophysics General Assembly(2003),predictability studies in China have made significant progress.For dynamic forecasts,two novel approaches of conditional nonlinear optimal perturbation and nonlinear local Lyapunov exponents were proposed to cope with the predictability problems of weather and climate,which are superior to the corresponding linear theory.A possible mechanism for the"spring predictability barrier"phenomenon for the El Ni(?)o-Southern Oscillation (ENSO)was provided based on a theoretical model.To improve the forecast skill of an intermediate coupled ENSO model,a new initialization scheme was developed,and its applicability was illustrated by hindcast experiments.Using the reconstruction phase space theory and the spatio-temporal series predictive method, Chinese scientists also proposed a new approach to improve dynamical extended range(monthly)prediction and successfully applied it to the monthly-scale predictability of short-term climate variations.In statistical forecasts,it was found that the effects of sea surface temperature on precipitation in China have obvious spatial and temporal distribution features,and that summer precipitation patterns over east China are closely related to the northern atmospheric circulation.For ensemble forecasts,a new initial perturbation method was used to forecast heavy rain in Guangdong and Fujian Provinces on 8 June 1998.Additionally, the ensemble forecast approach was also used for the prediction of a tropical typhoons.A new downscaling model consisting of dynamical and statistical methods was provided to improve the prediction of the monthly mean precipitation.This new downsealing model showed a relatively higher score than the issued operational forecast. 相似文献
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本文初步探讨了非线性局部Lyapunov指数方法(NLLE)在目标观测中的应用。首先, 在NLLE理论基础上研究了非线性动力系统内局部平均误差相对增长(LAGRE)特征, 证明了在误差发展进入随机状态前, LAGRE与初始误差大小无关而是与初始状态有关;在演化进入随机状态后, LAGRE的饱和值由初始误差大小决定这一特征。同时利用三个变量的常微分方程模型Lorenz63验证了这一结论。其次, 从非线性局部误差增长理论出发, 在局部动力演化相似方法(LDA)的基础上提出向前局部动力演化相似方法(FLDA)的概念, 并通过两个混沌个例来说明LDA和FLDA方法能够有效的利用历史资料还原任意初始状态的LAGRE。这些方法的提出为NLLE理论应用于观测资料研究目标观测问题提供了依据。 相似文献