太阳强迫厄尔尼诺/南方涛动充电振子模型的Hopf分岔与混沌

本文研究了一类太阳强迫的厄尔尼诺/南方涛动(ENSO)充电振子数理模型,通过数学变换将此ENSO振子方程组变换为有周期强迫项的van der Pol-Duffing方程,利用谐波平衡法定性分析得到此ENSO系统发生Hopf分岔的条件并做简单数值模拟,结果发现随着强迫作用增大,11年周期太阳循环强迫的ENSO系统经历准周期、倍频锁相到混沌的过程.     

海-气振子ENSO模型的同伦解法

研究了一个厄尔尼诺-南方海涛(ENSO)的时滞振子的模型.利用同伦映射方法求出了ENSO模型的近似解 关键词： 非线性 同伦 ENSO模型     

Modified variational iteration method for an El Ni no Southern Oscillation delayed oscillator

This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Niño Southern Oscillation. The approximate expansions of the delayed differential equation's solution are obtained successfully by the modified variational iteration method. The numerical results illustrate the effectiveness and correctness of the method by comparing with the exact solution of the reduced model.     

Self-organized criticality in the El Niño Southern oscillation

The Fourier analysis has been applied to observational sea surface temperature (SST) data from the Southern Pacific. The spectral response of the daily temperature fluctuations indicates that the so-called El Niño Southern Oscillation (ENSO) belongs to the class of dynamical phenomena which are in a self-organized critical state. This has implications on the predictability of the significant events in the ocean-atmosphere interaction process. A toy model is used to point out the similarities of this system with other large scale phenomena, as earthquakes and volcanic eruptions, which are considered to be consistent with the hypothesis of self-organized criticality. The qualitative agreement between observational data and results of numerical simulations demonstrates the validity extent of the theoretical approach.     

Noise-induced chaos in non-linear dynamics of El Niños

Motivated by an important practical significance, we analyze the noise-induced El Niño evolutionary equations. Our analysis based on the evaluation of largest Lyapunov exponents demonstrates the new effects of deterministic and stochastic dynamics of the El Niño–Southern Oscillation Events. We show that the non-linear deterministic model possesses either a multiturn limit cycle with regular self-oscillations or chaotic oscillations depending on slight variations of one of the main system parameters – the mean tropical easterlies. It is revealed that in the presence of noise, transformations of regular oscillations into chaotic ones are observed.     

Analyzing complex networks evolution through Information Theory quantifiers

A methodology to analyze dynamical changes in complex networks based on Information Theory quantifiers is proposed. The square root of the Jensen-Shannon divergence, a measure of dissimilarity between two probability distributions, and the MPR Statistical Complexity are used to quantify states in the network evolution process. Three cases are analyzed, the Watts-Strogatz model, a gene network during the progression of Alzheimer's disease and a climate network for the Tropical Pacific region to study the El Niño/Southern Oscillation (ENSO) dynamic. We find that the proposed quantifiers are able not only to capture changes in the dynamics of the processes but also to quantify and compare states in their evolution.     

The homotopic mapping method for sea-air oscillator model of interdecadal climate fluctuations

The E1 Nifio/La Nifia Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a coupled system of sea-air oscillator model is studied. The aim is to create an asymptotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the method of homotopic mapping, the approximate solution of corresponding problem is studied. It is proven from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.     

Topological phase transition and electrically tunable diamagnetism in silicene

The movement and relaxation of the localized energy on FPU lattices have been studied by using Wavelet transforms methods. The energy relaxation mechanism for nonlinear chains involves the degradation of higher frequency excitations into lower frequencies. It is shown that low frequency modes decay more slowly in nonlinear chains. The wavelet spectrum exhibits a behavior involving the interplay of phonon modes and breather modes.     

The continuous wavelet derived by smoothing function and its application in cosmology

The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet functions are obtained by taking the first derivative of smoothing functions with respect to the scale parameter. Due to this wavelet constructing scheme, the inverse transforms are only one-dimensional integrations with respect to the scale parameter, and hence the continuous wavelet transforms(CWTs) constructed in this way are more ready to use than the usual scheme. We then apply the Gaussian-derived wavelet constructed by our scheme to computations of the density power spectrum for dark matter, the velocity power spectrum and the kinetic energy spectrum for baryonic fluid. These computations exhibit the convenience and strength of the CWTs. The transforms are very easy to perform, and we believe that the simplicity of our wavelet scheme will make CWTs very useful in practice.     

一类厄尔尼诺海-气振子机理的同伦解法

研究了一类厄尔尼诺-南方海涛(ENSO)机理耦合系统振荡.利用同伦理论和摄动方法，较简便地得到了一类ENSO模型解的近似展开式. 关键词： 非线性 同伦理论 摄动 厄尔尼诺-南方海涛模型     

Tsallis’ statistics in the variability of El Niño/Southern Oscillation during the Holocene epoch

Analysis of the Tsallis q-triplet for the variability of El Niño Southern Oscillation (ENSO) index during the Holocene epoch (last 11,000 years) is presented. Three periods are analyzed, 0-7000, 7000-9700, 9700-11,000 years before the present. During the first and the third periods, the q-index values have the expected usual relations between them (q_sens<1<q_stat<q_rel), and in the second one there is an inversion between q_stat and q_rel (q_stat>q_rel).     

Thirteen years of atmospheric carbon dioxide measurements at Mt. Cimone station, Italy

Summary The atmospheric carbon dioxide concentration has been continuously measured at Mt. Cimone station from March 1979. In this paper a selection scheme is applied to the measured concentrations in order to obtain data representative of background conditions. Monthly averages, expressed in the WMO X-85 scale are calculated from the selected data and analysed by a technique of time series decomposition until december 1991. Monthly values exibit an increasing long-term trend, mainly due to the fossil fuel combustion: over the whole monitoring period the average CO₂ growth rate is 1.66 p.p.m.v./y. A seasonal cycle, largely due to the biospheric activity of the northern hemisphere is evident. The estimated average peak-to-peak amplitude is 11.32 p.p.m.v. with a maximum occurring in April and a minimum in August. The seasonal amplitude is found to be decreasing with time, by about 1.5 p.p.m.v. over the entire record: no conclusive interpretations are given about this experimental result. Besides the long-term trend and the seasonal cycle, CO₂ interannual variations are observed in the selected record; these correlate negatively with the Southern Oscillation Index (SOI) with a maximum correlation coefficient of 0.6 for a delay of about 7–8 months.     

Low-dimensional nonlinearity of ENSO and its impact on predictability

Using a hybrid coupled model, we perform a bred vector (BV) analysis and retrospective ENSO (El Niño and the Southern Oscillation) forecast for the period from 1881 to 2000. The BV local dimension and BV-skewness inherent to the intensity of nonlinearity are analyzed. Emphasis is placed on exploring the nature of the low-dimensional nonlinearity of the ENSO system and the relationship between BV-skewness and model prediction skills. The results show that ENSO is a low-dimensional nonlinear system, and the BV-skewness is a good measure of its predictability at the decadal/interdecadal time scales. As the low-dimensional nonlinearity of ENSO is weakened, high predictability is attained, and vice versa. The low-dimensional nonlinearity of ENSO is also investigated and verified using observations.Another finding in this study is the relationship between the error growth rate (BV-rate) and actual prediction skill. While there is a good positive correlation between them in some decades, the BV-rate demonstrates a strong inverse correlation with the prediction skill in other decades. The BV-rate components contributed by the nonlinear process play a dominant role in quantifying ENSO predictability. The possible mechanism for the link between BV-rate, BV-skewness and ENSO predictability is discussed.     

Determination of the characteristics of the spectra of neutron scattering for tungsten using the wavelet transform

The problem of the determination of the spectral characteristics using the lifting scheme with the linear approximation of signals and the Haar wavelet-transform algorithm (à trous algorithme) is considered. These transforms are recommended for use in combination with standard methods. Based on analysis of the behavior of the wavelet coefficients, a method to localize the peaks and to determine the positions of maxima is proposed. The efficiency of the use of non-traditional wavelet transforms for the filtration and compression of spectral data and the localization of peaks, in particular, for neutron-scattering spectra, is demonstrated.     

Tomograms, Wavelets, and Quasidistributions in the Geometric Picture

Different types of integral transforms of the analytic signal employed in information processing are studied within the framework of a new unified approach. They include tomographic probabilities, wavelet transform, Ville–Wigner function, etc. The connection of a vector (analytic signal) with projections of the transformed vector onto different axes in the signal space provides different integral transforms. The tomogram of the analytic signal is introduced by means of average Dirac (or Kronecker) delta-function of Hermitian operator. The relations of the wavelet and the Ville–Wigner quasidistribution to time–frequency, time--scale, and frequency–scale tomograms are studied.     

Variational iteration method for solving the mechanism of the Equatorial Eastern Pacific El Nino-Southern Oscillation

A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.     

Polar Wavelet Transform and the Associated Uncertainty Principles

The polar wavelet transform– a generalized form of the classical wavelet transform has been extensively used in science and engineering for finding directional representations of signals in higher dimensions. The aim of this paper is to establish new uncertainty principles associated with the polar wavelet transforms in \(L^{2}(\mathbb R^{2})\). Firstly, we study some basic properties of the polar wavelet transform and then derive the associated generalized version of Heisenberg–Pauli–Weyl inequality. Finally, following the idea of Beckner (Proc. Amer. Math. Soc. 123, 1897–1905 1995), we drive the logarithmic version of uncertainty principle for the polar wavelet transforms in \(L^{2}(\mathbb R^{2})\).     

基于小波分析的马铃薯地上生物量估算

地上生物量（AGB）是作物长势评价及产量预测的重要指标,因此快速准确地估算AGB至关重要。由于传统植被指数（VIs）估算多生育期的AGB存在饱和现象,因此,利用VIs结合基于离散小波转换（DWT）的影像小波分解（IWD）技术提取的高频信息和连续小波转换（CWT）技术提取的小波系数,探究VIs,VIs+IWD和VIs+CWT对于AGB的估算能力。首先,基于无人机平台分别获取马铃薯现蕾期、块茎形成期、块茎增长期、淀粉积累期的数码影像和成像高光谱影像以及地面实测的AGB数据。其次,利用数码影像通过IWD技术提取3种高频信息和利用高光谱反射率数据通过CWT技术提取小波系数以及构建6种高光谱植被指数。然后,将植被指数、高频信息和小波系数分别与AGB进行相关性分析,并挑选出不同尺度下相关系数绝对值较高的前10波段。最后,以VIs,VIs+IWD和VIs+CWT这3种变量分别使用偏最小二乘回归（PLSR）方法构建AGB估算模型,并对比不同模型估算AGB的效果。结果表明: （1）每个生育期选取的6种植被指数、3种高频信息和10种小波系数与AGB的相关性均达到0.01显著水平,整个生育期相关性均呈现先升高后降低的趋势,其中以小波系数得到的相关性最高、高频信息次之,植被指数最低。（2）对比分析每个生育期的3种估算模型,以VIs+CWT为输入变量的估算效果最好,VIs+IWD的估算效果次之,而VIs的估算效果最差,说明基于小波分析构建的模型适用性较广、稳定性较强。（3）每个生育期分别以3种变量利用PLSR方法构建的AGB估算模型均在块茎增长期达到最高精度（VIs：建模R2=0.70,RMSE=98.88 kg·hm-12,NRMSE=11.63%;VIs+IWD：建模R2=0.78,RMSE=86.45 kg·hm-12,NRMSE=10.17%;VIs+CWT：建模R2=0.85,RMSE=74.25 kg·hm-12,NRMSE=9.27%）。通过VIs分别结合IWD和CWT技术利用PLSR建模方法,可以提高AGB估算精度,为农业指导管理提供可靠参考。     

基于连续小波变换的地下天然气微泄漏点识别模型

天然气作为一种清洁、高效的低碳能源，消费占比日益增大。无论是地下输气管道还是储气库，由于管道腐蚀、老化、自然灾害，地下断层、注入井封存不好等因素，都会导致天然气泄漏。从安全、经济、环境等方面考虑，开展地下天然气管道和储气库微泄漏检测是十分必要的。利用高光谱遥感监测地表植被变化而间接探测天然气微泄漏点，通过野外可控系统模拟地下储存天然气微泄漏实验，以冬小麦为研究对象，采集了9期小麦冠层光谱数据，通过光谱分析探寻胁迫小麦光谱特征并构建指数识别模型。首先对小麦冠层光谱进行奇异值剔除和平滑处理，对连续统去除之后的冠层光谱进行连续小波变换，选用Mexihat母小波，在尺度参数为32时，小波系数有较少的峰值和谷值，能与原始光谱拟合较好，且小麦多期数据其峰值和谷值位置都比较稳定。受胁迫和健康小麦的原始光谱可分性较差，但小波系数在487，550和770 nm处受胁迫与健康小麦样本可分性较优，且具有明显的诊断性特征：(1）受胁迫和健康小麦的小波系数在487 nm处为“吸收谷”，其小波系数值为负值，健康小麦小波系数值大于受胁迫小麦的；(2）受胁迫和健康小麦的小波系数在550和770 nm处，有明显的“反射峰”，且受胁迫小麦的小波系数值较大。为更好突出差异性，增强受胁迫和健康小麦的小波系数差异特征，构建了CWT_mexh（CWT_mexh=CW2₇₇₀/(1-CW₄₈₇)·CW₅₅₀）指数用于胁迫与健康小麦的识别；然后分别与NDVI₇₀₅，mNDVI₇₀₅，ARI1，R₄₄₀/R₇₄₀，D₇₂₅/D₇₀₂指数进行对比分析，经J-M距离定量检验，结果显示CWT_mexh指数对天然气微泄漏胁迫下的冬小麦具有较好的识别效果，该指数在天然气胁迫发生20 d后可以稳定区分胁迫和健康两类小麦，且在全生育期都保持相同的规律，而NDVI₇₀₅，mNDVI₇₀₅，ARI1等指数在整个生育期内无法准确识别健康与胁迫小麦。CWT_mexh指数在稳定性、普适性与可识别性方面优于其他5个指数。因此，高光谱遥感监测地表植被间接识别天然气微泄漏点具有可行性，研究结果可为星载高光谱遥感监测地下储存天然气泄漏点提供理论依据和技术支持。     

选择性埋氧层上硅器件的单粒子瞬态响应的温度相关性

本文建立了90 nm工艺下的绝缘体上硅浮体器件和选择性埋氧层上硅器件模型,通过器件电路混合仿真探究了工作温度对上述两种结构的多级反相器链单粒子瞬态脉冲宽度以及器件内部电荷收集过程的影响.研究表明, N型选择性埋氧层上硅器件相较于浮体器件具有更好的抗单粒子能力,但P型选择性埋氧层上硅器件的抗单粒子能力在高线性能量转移值下与浮体器件基本相同.同时电荷收集的温度相关性分析表明,N型选择性埋氧层上硅器件只存在漂移扩散过程,当温度升高时其电荷收集量变化很小,而N型浮体器件存在双极放大过程,电荷收集量随着温度的升高而显著增加;另外, P型选择性埋氧层上硅器件和浮体器件均存在双极放大过程,当温度升高时P型选择性埋氧层上硅器件衬底中的双极放大过程越来越严重,由于局部埋氧层的存在,反而抑制了其源极的双极放大过程,导致它的电荷收集量要明显少于P型浮体器件.因此选择性埋氧层上硅器件比浮体器件更好地抑制了温度对单粒子瞬态脉冲的影响.