Shock solution for a class of nonlinear elliptic equation

The boundary value problem for the nonlinear elliptic equation is considered. The outer solution for the original problem is obtained. The boundary and interior layer correction terms are constructed by introducing stretched variables and setting local coordinate systems near the boundary and interior discontinuous point of outer solution. Under suitable conditions, using the differential inequalities and the mean value theorem, the existence of the shock solution for boundary value problem is proved and the asymptotic behavior of the solution is studied.     

Reaction diffusion equations for nonlinear boundary conditions

A class of singularly perturbed initial boundary value problems of reaction diffusion equations for nonlinear boundary conditions is considered.Under suitable conditions,by using the theory of differential inequalities,the existence and asymptotic behavior of solution for initial boundary value problem are studied.Moreover,the obtained solution indicates that there are initial and boundary layers,and the thickness of the initial layer is less than that of the boundary layer.     

Accurate Parallel Algorithm for Adini Nonconforming Finite Element

Multi-parameter asymptotic expansions are interesting since they justify the use of multi-parameter extrapolation which can be implemented in parallel and are well studied in many papers for the conforming finite element methods. For the nonconforming finite element methods, however, the work of the multi-parameter asymptotic expansions and extrapolation have seldom been found in the literature. This paper considers the solution of the biharmonic equation using Adini nonconforming finite elements and reports new results for the multi-parameter asymptotic expansions and extrapolation. The Adini nonconforming finite element solution of the biharmonic equation is shown to have a multi-parameter asymptotic error expansion and extrapolation. This expansion and a multi-parameter extrapolation technique were used to develop an accurate approximation parallel algorithm for the biharmonic equation. Finally, numerical results have verified the extrapolation theory.     

Boundary Perturbed Problem for Reaction Diffusion Time Delay Equation with Two Parameters

The singular perturbation problem for reaction diffusion time delay equation with boundary perturbation is considered. Firstly, the outer solution for the initial boundary value problem is constructed. Then, the initial and boundary layer correction terms are obtained using the stretched variables transforms. Finally, the asymptotic behavior of solution for the initial boundary value problem is studied.     

Car-following models of vehicular traffic

The Car-following model is a kind of microscopic simulation model for vehicular traffic, which describe the one-by-one following behaviors of vehides in the same traffic lane. As a common traffic phenomenon, following behavior is of great importance in the micro-study of intelligent traffic control.Compared with other traffic-flow models, car-following model embodies the human factors and feflects the real traffic sit-uation in a better way. This paper gives a systematic review of the development and actuality of car-following models by introducing and analyzing in detail the advantages and disavantages of GHR model, OV model,CA model and fuzzy-logic model. In addition, local stability and asymptotic stability of car-following models are discussed in this paper.     

A multi-soliton solution of the DNLS equation based on pure Marchenko formalism

By means of some algebraic techniques,especially the Binet-Cauchy formula,an explicit multi-soliton solution of the derivative nonlinear Schrdinger equation with vanishing boundary condition is attained based on a pure Marchenko formalism without needing the usual scattering data except for given N simple poles. The one-and two-soliton solutions are given as two special examples in illustration of the general formula of multi-soliton solution. Their effectiveness and equivalence to other approaches are also demonstrated. Meanwhile,the asymptotic behavior of the multi-soliton solution is discussed in detail. It is shown that the N-soliton solution can be viewed as a summation of N one-soliton solutions with a definite displacement and phase shift of each soliton in the whole process(from t →∞ to t → +∞ ) of the elastic collisions.     

Asymptotic Behavior of a Stochastic SIRS Model with Non-linear Incidence and Levy Jumps

A stochastic susceptible-infective-recovered-susceptible（ SIRS） model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito＇s formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0〈 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0〉 1,it fluctuates around the endemic equilibrium of the deterministic model.     

A variational iteration method for studying the ENSO mechanism

A coupled system of the El Ni(n)o/La Ni(n)o-Southern Oscillation (ENSO) mechanism is studied. Using the variational iteration theory, the approximations of the solution of an ENSO model is obtained.     

Instrumental variable type estimation for generalized varying coefficient models with error-prone covariates

In this paper,the estimation for a class of generalized varying coefficient models with error-prone covariates is considered.By combining basis function approximations with some auxiliary variables,an instrumental variable type estimation procedure is proposed.The asymptotic results of the estimator,such as the consistency and the weak convergence rate,are obtained.The proposed procedure can attenuate the effect of measurement errors and have proved workable for finite samples.     

Consistency and asymptotic normality of MLE of parameter vector in a randomly censored GLM with incomplete information

The generalized linear model（GLM） based on the observed data with incomplete information in the case of random censorship is defined. Under the given conditions, the existence and uniqueness of the solution on the likelihood equations with respect to the parameter vector β of the model are discussed, and the consistency and asymptotic normality of the maximum likelihood estimator（MLE） βn^-, are proved.     

Asymptotic behavior of perturbed solution for simple coupled ocean-atmosphere model for ENSO

The El Ni(n~)o/La Ni(n~)a and the Southern Oscillation are an interannual phenomenon involved in the tropical Pacific Ocean-atmosphere interactions. In this paper, based on a kind of simple coupled ocean-atmosphere model for ENSO, using the perturbed theory and method, the asymptotic behavior of solution of corresponding problem is studied. It is proved from the results that the trajectories of phase plane for coupled ocean-atmosphere model ultimately tend to the stable attractors separately.     

Variational iteration solving method of a sea-air oscillator model for the ENSO

A time delay equation for sea-air oscillator model is studied. The aim is to create an asymtotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the variational iteration method, the approximate solution of corresponding problem is obtained. It is proven from the results that the method of variational iteration method can be used for analyzing the sea surface temperature anomaly in the equatorial eastern Pacific of the atmosphere-ocean oscillation for ENSO model.     

Variational iteration solving method of a sea-air oscillator model for the ENSO

A time delay equation for sea-air oscillator model is studied. The aim is to create an asymtotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the variational iteration method, the approximate solution of corresponding problem is obtained. It is proven from the results that the method of variational iteration method can be used for analyzing the sea surface temperature anomaly in the equatorial eastern Pacific of the atmosphere-ocean oscillation for ENSO model.     

ENSO frequency change in coupled climate models as response to the increasing CO<Subscript>2</Subscript> concentration

The response of ENSO frequency to the increasing CO2 concentration and associated mechanism are examined with outputs of four coupled climate models (GFDL/CM2.0,CNRM/CM3,IPSL/CM4 and INM/CM3.0) submitted to the IPCC Fourth Assessment Report (IPCC AR4).Results reveal a significant change of ENSO frequency as response to the increasing CO2 concentration.However,such a change exhibits an evident model dependence.The ENSO frequency tends to increase in GFDL/CM2.0 and CNRM/CM3 models and decreases in IPSL/CM4 an...     

一类具有年龄结构非自治种群模型零平衡解的全局渐近稳定性

讨论一类具有年龄结构且死亡率与种群总数有关的非线性非自治种群模型解的渐近性态,证明了解的存在唯一性并得到了零平衡解稳定和全局稳定的充分条件.     

一类具有扩散种群的持续生存和渐近性

本利用上、下解和LyaPunov函数方法，讨论了一类具有扩散的种群模型的渐近性质，给出了具有重要生物学意义的结果．     

基于比率依赖的两种群捕食者—食饵系统的随机模型的渐近性质

在考虑有随机干扰的情况下,对基于比率依赖的两种群捕食者-食饵系统的性质进行了研究。首先通过随机微分方程理论建立此系统的随机模型,并利用构造V函数,结合停时、常用不等式、It?公式等技巧和方法对此系统的性质进行了讨论。最后,在假设条件下,得到了基于比率依赖的两种群捕食者-食饵系统的随机最终有界、解的渐近矩估计和轨道估计等性质。     

求解广义非线性互补问题的神经网络

研究了广义非线性互补问题，将其转化为等价的无约束优化问题，给出了求解它的二个神经网络模型．分析了新模型的平衡点与互补问题解的关系，证明了其稳定性和平衡．占、集的渐近稳定性，并给出了其渐近收敛的充分条件．新模型可用来求解一类非单调的问题．     

一类含脉冲接种且总人口在变化的传染病模型的渐近分析

讨论了一类具有比例接种和脉冲接种的传染病模型的渐近性态，给出了对疾病传播有重要影响的基本再生数。在连续预防接种下，利用广义的Dulac函数的方法证明了无病平衡点和地方病平衡点的全局稳定性，对脉冲接种下的SISV传染病模型，证明了无病周期解的存在性和全局渐近稳定性。