Determination of the Backward Predictability Limit and Its Relationship with the Forward Predictability Limit

In this work, two types of predictability are proposed—forward and backward predictability—and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively estimate the local forward and backward predictability limits of states in phase space. The forward predictability mainly focuses on the forward evolution of initial errors superposed on the initial state over time, while the backward predictability is mainly concerned with when the given state can be predicted before this state happens. From the results, there is a negative correlation between the local forward and backward predictability limits. That is, the forward predictability limits are higher when the backward predictability limits are lower, and vice versa. We also find that the sum of forward and backward predictability limits of each state tends to fluctuate around the average value of sums of the forward and backward predictability limits of sufficient states.Furthermore, the average value is constant when the states are sufficient. For different chaotic systems, the average value is dependent on the chaotic systems and more complex chaotic systems get a lower average value. For a single chaotic system,the average value depends on the magnitude of initial perturbations. The average values decrease as the magnitudes of initial perturbations increase.     

成矿元素巨量聚集的混沌机制——斑岩型和构造蚀变岩型矿床例析

成矿元素含量的变化受控于成矿系统内部的动力学过程,具有较强的随机性与混沌特征,对其变化特征的定量刻画有助于深入理解成矿过程,并为找矿预测提供理论依据。本文以三江普朗斑岩型铜矿的Cu元素与胶东大尹格庄构造蚀变岩型金矿的Au元素品位序列为研究对象,运用混沌时间序列分析法中的相空间重构技术、吸引子的关联维及最大Lyapunov指数解析了Cu与Au元素品位序列的分布特征。结果显示:斑岩型铜矿强矿化和中矿化Cu元素品位的饱和关联维介于4.42与9.69之间,饱和嵌入维介于25与28之间,最大Lyapunov指数介于0.0021与0.0661之间,弱矿化勘探线Cu元素关联维没有出现饱和现象,最大Lyapunov指数随着嵌入维的增大,由正数变为负数;构造蚀变岩型金矿的强矿化勘探线Au元素的关联维为3.18,饱和嵌入维为23,最大Lyapunov指数为0.0082,而中矿化和弱矿化勘探线Au元素的关联维没有出现饱和现象,且随着嵌入维的增大,最大Lyapunov指数由正数变为负数,表明斑岩型中-强矿化地区的Cu元素和构造蚀变岩型强矿化区域的Au元素品位序列具有混沌动力学特征,而弱矿化地区的Cu元素及中弱矿化地区的Au元素品位序列则具有更强的随机性特征;同时,具有混沌特征的斑岩型铜矿的饱和嵌入维和关联维及最大Lyapunov指数的均值都大于蚀变岩型矿床,说明斑岩型铜矿比蚀变岩型矿床的元素具有更强混沌特性与更复杂的控制因素,如温度、硫化作用、流体不混溶、蚀变叠加等。     

月尺度气温可预报性对资料长度的依赖及可信度

利用全国518个站1960—2011年逐日气温观测资料和160个站1983—2012年月尺度气温客观预测数据,基于非线性局部Lyapunov指数和非线性误差增长理论,研究中国区域月尺度气温可预报性期限对资料序列长度的依赖性。结果表明:气温可预报性期限对资料序列的长度有一定程度的依赖性,在西北、东北及华中地区尤为明显。平均而言,45年的资料序列长度才能够得到稳定合理的可预报性期限。为了验证气温可预报期限计算结果的可信度,将月尺度气温的可预报性期限与客观气候预测方法的预报评分技巧进行对比,发现两者结果非常一致。其中,由观测资料得到的1月气温的可预报性期限明显低于7月,1月客观气候预测方法的预报评分技巧也明显低于7月,且1月 (7月) 预报评分的空间分布型与1月 (7月) 气温可预报性期限的空间分布型较为一致。因此,利用非线性局部Lyapunov指数和台站逐日观测资料分析气温的可预报性期限结果是可信的。     

非线性局部Lyapunov指数方法在目标观测中的应用初探

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。     

Alternative measures of dispersion applied to flow in a convoluted channel

Steady flow in a convoluted channel is studied via Particle Tracking Velocimetry. The channel is constructed from a sequence of closed parallel cylindrical tubes welded together in plane which are then sliced down the lateral mid-plane and the lower complex is laterally shifted relative to the upper complex. Flow is induced in the lateral direction normal to the axis of the tubes. The a-time, T_a, finite-size Lyapunov exponent, λ_a, and the real-space self- and distinct-part of the intermediate scattering functions, G_s and G_d, and the pair density function, G_p, are computed from the data. Particle trajectories, velocity maps and streamlines show the channel has two prominent recirculation zones and a main flow region. The first passage time probability density function of tagged particles past a plane transverse to the mean flow illustrates how particles are delayed by recirculation zones. The delay caused by fluid element folding is manifested in single particle statistics such as the first passage time and the slowing increase in horizontal evolution of G_s. G_p describes initial particle distribution and allows areas in the flow domain trapping particles to be identified and visualized. G_d shows the evolution of the average separation of pairs of particles and when examined in a recirculation zone, it evolves little because of fluid element rotation. λ_a gives information on what transpires at a fixed scale and provides an estimate of the rate at which particles initially separated by a distance x separate to a distance ax as opposed to G_d which allows one to view changes over time. At small separations, λ_1.3 approaches a constant and for intermediate separations it scales as x^−0.8.     

黑河流域地理观测分析——复杂性科学视角（英文）

Since 2005,dozens of geographical observational stations have been established in the Heihe River Basin(HRB),and by now a large amount of meteorological,hydrological,and ecological observations as well as data pertaining to water resources,soil and vegetation have been collected.To adequately analyze these available data and data to be further collected in future,we present a perspective from complexity theory.The concrete materials covered include a presentation of adaptive multiscale filter,which can readily determine arbitrary trends,maximally reduce noise,and reliably perform fractal and multifractal analysis,and a presentation of scale-dependent Lyapunov exponent(SDLE),which can reliably distinguish deterministic chaos from random processes,determine the error doubling time for prediction,and obtain the defining parameters of the process examined.The adaptive filter is illustrated by applying it to obtain the global warming trend and the Atlantic multidecadal oscillation from sea surface temperature data,and by applying it to some variables collected at the HRB to determine diurnal cycle and fractal properties.The SDLE is illustrated to determine intermittent chaos from river flow data.     

Analyses of geographical observations in the Heihe River Basin: Perspectives from complexity theory

Journal of Geographical Sciences - Since 2005, dozens of geographical observational stations have been established in the Heihe River Basin (HRB), and by now a large amount of meteorological,...     

含辐射和扁率的圆型限制性三体问题的轨道稳定性研究

基于最小二乘法原理的速度因子方法是保流形结构算法中效率最高、稳定性最好、应用最广的方法.利用速度因子方法讨论了主星为辐射源,伴星为扁球的平面圆型限制性三体问题的稳定性问题.数值研究表明:(1)仅考虑扁状摄动项时,系统混沌运动的轨道数量会增多;(2)仅考虑辐射项时,系统有序运动的轨道数量会增多;(3)同时存在辐射和扁状摄动时,辐射占主导作用,系统有序运动的几率会增加.     

南沙群岛海域近海面大气湍流混沌特性

混沌概念的提出,有必要研究大气湍流是否具有混沌行为。根据1994年9月18—30日南沙群岛海域渚碧礁（10°52＇N,114°04＇E）的近海面大气水平风速及气温的观测资料,计算和分析了有关诊断系统是否是混沌运动的特征量：关联维数、Lyapunov指数和关联熵。结果表明,南沙群岛海域近海面大气湍流是一种混沌运动。同时给出并讨论了其它一些结论。     

Practical control of underactuated ships

This paper presents a design of global smooth controllers that achieve the practical stabilization of arbitrary reference trajectories, including fixed points and nonadmissible trajectories for underactuated ships. These ships do not have an independent actuator in the sway axis. The control design is based on several nonlinear coordinate changes, the transverse function approach, the back-stepping technique, the Lyapunov direct method, and utilization of the ship dynamics. Simulation results illustrate the effectiveness of the proposed control design.