PERTURBED SOLUTION OF SEA-AIR OSCILLATOR FOR THE EL NI O/LA NI O-SOUTHERN OSCILLATION MECHANISM

The El Nino/La Nino-Southern Oscillation(ENSO)is an interannual phenomenon in-volved in the tropical Pacific ocean-atmosphere interactions.Phenomenon of the ENSO is avery attractive object of study in the international academic circles[1-6].Lin et al.cons…     

PERTURBED SOLUTION OF SEA-AIR OSCILLATOR FOR THE EL NINO/LA NINO-SOUTHERN OSCILLATION MECHANISM

A class of coupled system to oscillate of the E1 Nino/La Nino-Southern Oscillation （ENSO） mechanism is studied. Using the perturbed theory, the asymptotic expansions and asymptotic behavior of the solution for an ENSO model are obtained.     

Asymptotic solution for EI Ni$$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{n} $$o-southern oscillation of nonlinear model

A class of nonlinear coupled system for EI Nino-Southern Oscillation （ENSO） model is considered. Using the asymptotic theory and method of variational iteration, the asymptotic expansion of the solution for ENSO models is obtained.     

A CLASS OF HOMOTOPIC SOLVING METHOD FOR ENSO MODEL

The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models.And on the basis of a class of oscillator of ENSO models,using the method of homotopic mapping,the approximation of solution of corresponding problem is stud- ied.It is proved from the results that homotopic method can be used for analyzing the SST anomaly...     

厄尔尼诺/拉尼娜-南方海涛模型的变分迭代解法

研究了-类厄尔尼诺-南方海涛（ENSO）振子的模型，利用变分迭代方法求出了ENSO模型的近似解。     

Ocean-Atmosphere Interaction in the Lifecycle of ENSO： The Coupled Wave Oscillator

To explain the oscillatory nature of E1 Nino/Southern Oscillation （ENSO）, many ENSO theories emphasize the free oceanic equatorial waves propagating/reflecting within the Pacific Ocean, or the discharge/recharge of Pacific-basin-averaged ocean heat content. ENSO signals in the Indian and Atlantic oceans are often considered as remote response to the Pacific SST anomaly through atmospheric teleconnections. This study investigates the ENSO life cycle near the equator using long-term observational datasets. Space-time spectral analysis is used to identify and isolate the dominant interannual oceanic and atmospheric wave modes associated with ENSO. Nino3 SST anomaly is utilized as the ENSO index, and lag-correlation/regression are used to construct the composite ENSO life cycle. The propagation, structure and feedback mechanisms of the dominant wave modes are studied in detail. The results show that the dominant oceanic equatorial wave modes associated with ENSO are not free waves, but are two ocean-atmosphere coupled waves including a coupled Kelvin wave and waves are not confined only to the Pacific a coupled equatorial Rossby （ER） wave. These Ocean, but are of planetary scale with zonal wavenumbers 1-2, and propagate all the way around the equator in more than three years, leading to the longer than 3-year period of ENSO. When passing the continents, they become uncoupled atmospheric waves. The coupled Kelvin wave has larger variance than the coupled ER wave, making the total signals dominated by eastward propagation. Surface zonal wind stress （x） acts to slow down the waves. The two coupled waves interact with each other through boundary reflection and superposition, and they also interact with an off-equatorial Rossby wave in north Pacific along 15N through boundary reflection and wind stress forcing. The precipitation anomalies of the two coupled waves meet in the eastern Pacific shortly after the SST maximum of ENSO and excite a dry atmospheric Kelvin wave which quickly circles the whole equator and leads to a zonally symmetric signal of troposphere temperature. ENSO signals in the Indian and Atlantic oceans are associated with the two coupled waves as well as the fast atmospheric Kelvin wave. The discharge/recharge of Pacific-basin-averaged ocean heat content is also contributed by the two coupled waves. The above results suggest the presence of an alternative coupled wave oscillator mechanism for the oscillatory nature of ENSO.     

A wavelet cross-spectral analysis of solar–ENSO–rainfall connections in the Indian monsoons

The possible connections between the El Nino-Southern Oscillation (ENSO) phenomenon and Indian monsoon rainfall have been widely discussed in the meteorological literature. We show strong statistical evidence here for connections of ENSO with solar activity. This is particularly evident in a comparison between the two contrasting test periods of 1878–1913 and 1933–1964, representing three complete cycles of lowest and highest solar activity respectively since 1850. Wavelet statistical analysis reveals that the link between solar activity and ENSO is generally stronger than that between ENSO and rainfall but only slightly weaker than that between solar activity and rainfall. Over the two test periods an increase in solar activity is associated with a decrease in ENSO indices and an increase in the monsoon rainfall in the 8–16 y period band. In the 2–7 y period band the effects vary with region. The net effect of solar processes on rainfall thus appears to be the result of counteracting or cooperating influences on shorter (about 5–6 y) and longer (about 11–12 y) time scales, the latter on the whole dominating over the former. The present analysis thus suggests that the influence of solar processes on Indian rainfall operates in part indirectly through ENSO, but on more than one time scale.     

赤道东太平洋海气耦合振荡的非线性分析及ENSO循环的极限环理论

把赤道东太平洋地区大气对流层，海洋混合层看作是在定常热源(太阳辐射)驱动下的动力系统，利用一个局域平均的热力学气候模式，建立了海气耦合自激振荡模型，得到了一个封闭的自治的二次系统，对系统进行了线性和非线性分析．结合系统稳定的极限环解，对海气耦合的物理机制进行了探讨．和观测事实的比较表明，在赤道东太平洋区域平均的以500hPa为代表的大气对流层的温度距平和海表温度距平，在相平面上和极限环解定性上很一致．这为研究热带海气相互作用的年际变化提供了一个理论模型．     

Interannual variations in the length of day and ENSO events in 1982—1983 and 1997—1998

The length of day series during the period of 1962.0—2000.0, the atmospheric angular momentum and the Southern Oscillation Index are adopted to analyze the relationships among the ENSO events that have occurred since 1960, the changes in the length of day and the atmospheric angular momentum. Attention is particularly given to the different effects of the 1982—1983 and 1997—1998 ENSO events on the variations of Earth rotation. The synthetic excitation effects of multi-scale atmospheric oscillations on the anomalous variations of the interannual rates of Earth rotation are revealed by means of the time-frequency spectrum of the wavelet transform.     

一类海-气振子ENSO模型的同伦分析解法

研究了一个ENSO海-气时滞振子模型.利用同伦分析方法,得到了该模型解的近似展开式,通过与特殊情况下的精确解比较,得到的二级近似解具有较高的精度.     

Interannual variations in the length of day and ENSO events in 1982–1983 and 1997–1998

The length of day series during the period of 1962.0–2000.0, the atmospheric angular momentum and the Southern Oscillation Index are adopted to analyze the relationships among the ENSO events that have occurred since 1960, the changes in the length of day and the atmospheric angular momentum. Attention is particularly given to the different effects of the 1982–1983 and 1997–1998 ENSO events on the variations of Earth rotation. The synthetic excitation effects of multi-scale atmospheric oscillations on the anomalous variations of the interannual rates of Earth rotation are revealed by means of the time-frequency spectrum of the wavelet transform.     

一类小周期椭圆方程的三重尺度渐近分析

利用三重尺度方法对一类小周期椭圆方程进行了三重尺度渐近展开分析,构造了对应的三重尺度形式渐近展开式,得到了均匀化常数和均匀化方程.在形式渐近展开的基础上,构造了对应边值问题解的三重尺度渐近近似解,并分析了对应三重尺度形式渐近误差估计.     

Mathematical Analysis of the Jin-Neelin Model of El Niño-Southern-Oscillation

The Jin-Neelin model for the El Ni$\wt{\rm n}$o--Southern Oscillation (ENSO for short) is considered for which the authors establish existence and uniqueness of global solutions in time over an unbounded channel domain. The result is proved for initial data and forcing that are sufficiently small. The smallness conditions involve in particular key physical parameters of the model such as those that control the travel time of the equatorial waves and the strength of feedback due to vertical-shear currents and upwelling; central mechanisms in ENSO dynamics. From the mathematical view point, the system appears as the coupling of a linear shallow water system and a nonlinear heat equation. Because of the very different nature of the two components of the system, the authors find it convenient to prove the existence of solution by semi-discretization in time and utilization of a fractional step scheme. The main idea consists of handling the coupling between the oceanic and temperature components by dividing the time interval into small sub-intervals of length $k$ and on each sub-interval to solve successively the oceanic component, using the temperature $T$ calculated on the previous sub-interval, to then solve the sea-surface temperature (SST for short) equation on the current sub-interval. The passage to the limit as $k$ tends to zero is ensured via a priori estimates derived under the aforementioned smallness conditions.     

关于渐近循环马氏链泛函的强大数定律

研究了一类非齐次马氏链———渐近循环马氏链泛函的强大数定律,首先引出了渐近循环马氏链的概念,然后给出了若干引理.利用了渐近循环马氏链关于状态序偶出现频率的强大数定理给出并证明了关于渐近循环马氏链泛函的强大数定律,所得定理作为推论可得到已有的结果.     

强混合样本下最近邻密度估计的渐近正态性

研究了α-混合样本下最近邻密度估计的渐近性质,证明了估计的渐近正态性并且给出了其渐近方差的显式表达式,由此构造了α-混合样本下概率密度的渐近置信区间.     

Strong laws of large numbers for asymptotic even–odd Markov chains indexed by a homogeneous tree

In this paper, we are going to study the strong laws of large numbers for asymptotic even–odd Markov chains indexed by a homogeneous tree. First, the definition of the asymptotic even–odd Markov chain is introduced. Then the strong limit theorem for asymptotic even–odd Markov chains indexed by a homogeneous tree is established. Next, the strong laws of large numbers for the frequencies of occurrence of states and ordered couple of states for asymptotic even–odd Markov chains indexed by a homogeneous tree are obtained. Finally, we prove the asymptotic equipartition property (AEP) for these Markov chains.     

Asymptotic speed of spread and traveling fronts for a nonlocal reaction–diffusion model with distributed delay

In this paper, a nonlocal reaction–diffusion model with distributed delay is studied. The asymptotic speed of spread is established for this model, and its coincidence with the minimal wave speed for traveling wave fronts is proved. Moreover, the dependence of the asymptotic speed of spread on delay and the nonlocal effect is considered. Our main finding here is that the delay can induce slow asymptotic speed of spread while the nonlocal effect can increase fast asymptotic speed of spread.     

Asymptotic stability analysis of autonomous systems by applying the method of localization of compact invariant sets

The asymptotic stability and global asymptotic stability of equilibria in autonomous systems of differential equations are analyzed. Conditions for asymptotic stability and global asymptotic stability in terms of compact invariant sets and positively invariant sets are proved. The functional method of localization of compact invariant sets is proposed for verifying the fulfillment of these conditions. Illustrative examples are given.     

On asymptotic equivalence of linear and quasilinear difference equations

The asymptotic equivalence of systems of difference equations of linear and quasilinear type is investigated. The first result on the asymptotic equivalence of linear systems is a discrete analog of an improved version of the Levinson's well-known theorem on asymptotic equivalence of linear differential equations, while the second one providing conditions for asymptotic equivalence of linear and quasilinear systems is related to that of Yakubovich in differential equations case.     

Asymptotic equivalence of probability distributions with applications to some problems of asymptotic independence

Summary The problem of asymptotic approximation is formulated in a generalized form, and the basic concepts of asymptotic equivalence of probability distributions, which are fundamental to the study of asymptotic approximation problems, are established precisely. For the purpose of practical applications, some useful criterions for the asymptotic equivalence are given.