基于Hurst指数的黑龙江省作物生长季降水趋势研究

基于黑龙江省78个气象站1971—2016年逐日降水资料,综合采用墨西哥帽小波分析、Hurst指数分析等方法,对黑龙江省作物生长季(5—9月)降水量变化和未来趋势进行分析及预测。结果表明:1971—2016年,黑龙江省生长季、5月、6月降水量存在7 a、14 a、7 a左右的主周期,7月、8月、9月降水量存在2 a、3 a、7 a左右的第1主周期及6 a、11 a、21 a左右的第2主周期,各月均存在最近几年降水偏多的趋势;作物生长季降水量年际间为波动式振荡变化,7月、8月振荡幅度相对较大。年代际变化总体存在增加—减少—增加趋势,20世纪80年代、90年代降水量普遍偏多,2010年以来出现急转升高变化;单站各月Hurst指数均在0.5以上,降水存在比较明显的赫斯特现象;降水主要出现在夏季且以7月最为集中,最近几年降水偏多、7月异常降水集中以及主要流域未来7月降水的持续增加趋势在农业防灾减灾上值得关注。     

变分原理和非线性Lyapunov稳定性判据

本文通过构造斜压大气运动的原始方程模式和两层模式的Hamilton守恒量及积分不变的Casimir泛函,并使用变分法,得到了斜压大气运动的非线性Lyapunov稳定性判据,这个判据是Arnold-Blumen-Zeng判据的推广。     

混沌系统单变量可预报性研究

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。     

一类非线性时变时滞随机大系统的稳定性

讨论了线性时滞随机系统平凡解的 几乎必然渐近稳定性&并推广到非线性 多时滞随机大系统的几乎必然渐近稳定 性''提出了非线性多时滞随机大系统几 乎必然渐近稳定性的代数判据''最后&用 仿真例子说明了主要结果的可行性与有 效性     

On bridges B(pL, qS) around triangular libration points

When μ is smaller than Routh’s critical value μ ₁ = 0.03852 . . . , two planar Lyapunov families around triangular libration points exist, with the names of long and short period families. There are periodic families which we call bridges connecting these two Lyapunov families. With μ increasing from 0 to 1, how these bridges evolve was studied. The interval (0,1) was divided into six subintervals (0, μ ₅), (μ ₅, μ ₄), (μ ₄, μ ₃), (μ ₃, μ ₂), (μ ₂, μ ₁), (μ ₁, 1), and in each subinterval the families B(pL, qS) were studied, along with the families B(qS, qS′). Especially in the interval (μ ₂, μ ₁), the conclusion that the bridges B(qS, qS′) do not exist was obtained. Connections between the short period family and the bridges B(kS, (k + 1)S) were also studied. With these studies, the structure of the web of periodic families around triangular libration points was enriched.     

基于障碍李雅普诺夫函数非线性系统的死区补偿控制

本文集中在带有部分状态约束的非线性单输入单输出系统的自适应控制器设计上.考虑了非对称死区的非线性输入特性,选取障碍李雅普诺夫函数用来阻止部分受约束的状态违反约束条件.根据障碍李雅普诺夫函数反步法,解决了该类系统的输出跟踪问题,同时也处理了死区非线性带来的影响.针对下三角结构的非线性系统,设计了自适应控制器,证明了闭环系统所有信号都是有界的,同时保证了系统输出可以跟踪上参考信号.最后,仿真结果表明了所提方法的有效性.     

高阶非线性系统自适应模糊有限时间状态约束控制

针对一类具有状态约束的非严格反馈高阶非线性系统,研究一种自适应模糊有限时间跟踪控制问题.首先,利用模糊逻辑系统逼近不确定性非线性函数,在此基础上,采用障碍Lyapunov函数,解决状态约束问题,通过障碍加幂积分方法和反步递推技术,提出了一种有限时间控制设计方法.在有限时间Lyapunov稳定意义下,严格证明闭环系统半全局实际有限时间稳定且系统的状态不超出给定的约束边界,并实现了有限时间跟踪控制目标.最后,仿真研究进一步验证了所提出控制方法的有效性.     

Nonlinear Coupled Motions for a Given Two-Point Tension Mooring System

—The nonlinear behaviors of plane coupled motions for a given two-point tension mooring sys-tem,are discussed in the present paper.For a cylinder moored by two taut lines under the action ofgravity,buoyance and forces due to wave-current and mooring lines,a mathematical model of motionswith three degrees of freedom is established.The steady solution and stability are analyzed.By integratingthe equations of motions,history,phase map and Poincare map are obtained.The Liapunov exponentsare also computed.The numerical results show that:the horizontal movement will increase,and stabilitywill also increase as the steady force increases.The amplitude of responses will decrease as time-dependentforces decrease.Because of the geometric nonlinearity,there exist many windows bifurcating to pseudo-pe-riodic or multi-periodic solution.The bifurcating patterns may be different.The behaviors are very com-plex.Under wave excitation alone,the motions are nonsymmetrical but still symmetrical statistically.     

岩性储集层的混沌识别技术研究

本文从动力学系统原理出发,论述了混沌理论中的李指数法,并从地震剖面上提取李指数,并应用李指数来区分和识别储集层的岩性变化特征和含油气性。计算和应用研究表明,李指数随着相空间维数的增加容易趋于稳定值,这就使它预测地震序列横向变化的可靠性增大,这正是李指数预测岩性和含油气性的一个优越性。成功地应用实例表明,混沌识别技术是岩性储集层的一种有效识别技术,并具有广阔的应用前景。     

Integrated evaluation of urban groundwater hydrogeochemistry in context of fractal behaviour of groundwater level fluctuations

The present study was carried out as part of a complex survey of urban groundwater quality and quantity in Szeged, southeast Hungary. The concentrations of 12 inorganic contaminants in 28 shallow groundwater monitoring wells were determined over a 2-year period (2010–2012). The evaluation of concentrations indicates remarkable contamination all over the city. Discriminant analysis (DA) was used to evaluate the spatial changes of groundwater quality. The groundwater levels were measured over a 14-year period (2000–2013). The fractal properties of water level fluctuations time series characterizing the groundwater system and Tisza River were investigated using rescaled range (R/S) analysis. The resulting Hurst exponents clearly showed the persistency and thus long memory effects of both the groundwater and the river flow. Comparison of the results of DA with the results of R/S analysis thus implies that the geological conditions and the changing groundwater quantities are not related to groundwater quality.

EDITOR A. Castellarin

ASSOCIATE EDITOR A. Fiori