Global behavior of a higher order nonlinear difference equation

In this paper, we consider a higher order difference equation of the form

     

基于年龄分组的单种群收获模型及稳定性分析

本文建立了一种按年龄分组的单种群收获模型 ,详细分析了该模型的稳定性 ,并得到了该模型临界稳定的充分必要条件 ,还得到了在临界稳定平衡中的极限状态解及临界稳定的生物学意义     

一类带有一般接触率和常数输入的流行病模型的全局分析

借助极限系统理论和构造适当的Liapunov函数,对带有一般接触率和常数输入的SIR型和SIRS型传染病模型进行讨论．当无染病者输入时,地方病平衡点存在的阈值被找到A·D2对相应的SIR模型,关于无病平衡点和地方病平衡点的全局渐近稳定性均得到充要条件;对相应的SIRS模型,得到无病平衡点和地方病平衡点全局渐近稳定的充分条件．当有染病者输入时,模型不存在无病平衡点．对相应的SIR模型,地方病平衡点是全局渐近稳定的;对相应的SIRS模型,得到地方病平衡点全局渐近稳定的充分条件．     

Global analysis of some epidemic models with general contact rate and constant immigration

An epidemic models of SIR type and SIRS type with general contact rate and constant immigration of each class were discussed by means of theory of limit system and suitable Liapunov functions. In the absence of input of infectious individuals, the threshold of existence of endemic equilibrium is found. For the disease-free equilibrium and the endemic equilibrium of corresponding SIR model, the sufficient and necessary conditions of global asymptotical stabilities are all obtained. For corresponding SIRS model, the sufficient conditions of global asymptotical stabilities of the disease-free equilibrium and the endemic equilibrium are obtained. In the existence of input of infectious individuals, the models have no disease-free equilibrium. For corresponding SIR model, the endemic equilibrium is globally asymptotically stable ; for corresponding SIRS model, the sufficient conditions of global asymptotical stability of the endemic equilibrium are obtained.     

Fluid-solid coupling mathematical model of contaminant transport in unsaturated zone and its asymptotical solution

IntroductionThetransportofcontaminantsinunsaturatedzonehascausedmuchattention .Inearly1960s,contaminationproblemsofsoilandgroundwaterhadbeenstudiedathomeandabroad[1].Andinrecentyears ,thetransformationandtransportationofcontaminantshavebeendeeplystudiedinthefieldsofhydrogeology ,petroleumengineering ,environmentalengineeringandsoon[2 ,3].Somecontaminanttransportmodelshavebeenpresentedsofar.Forexample ,Paker[4 ]etal.presentedaconstitutivemodelgoverningparametersofwater,gasandcontaminantswhenth…     

A delay-decomposition approach for stability of neural network with time-varying delay

This paper studies delay-dependent asymptotical stability problems for the neural system with time-varying delay. By dividing the whole interval into multiple segments such that each segment has a different Lyapunov matrix, some improved delay-dependent stability conditions are derived by employing an integral equality technique. A numerical example is given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Mathematical construction of a Reissner–Mindlin plate theory for composite laminates

A Reissner–Mindlin theory for composite laminates without invoking ad hoc kinematic assumptions is constructed using the variational-asymptotic method. Instead of assuming a priori the distribution of three-dimensional displacements in terms of two-dimensional plate displacements as what is usually done in typical plate theories, an exact intrinsic formulation has been achieved by introducing unknown three-dimensional warping functions. Then the variational-asymptotic method is applied to systematically decouple the original three-dimensional problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The resulting theory is an equivalent single-layer Reissner–Mindlin theory with an excellent accuracy comparable to that of higher-order, layer-wise theories. The present work is extended from the previous theory developed by the writer and his co-workers with several sizable contributions: (a) six more constants (33 in total) are introduced to allow maximum freedom to transform the asymptotically correct energy into a Reissner–Mindlin model; (b) the semi-definite programming technique is used to seek the optimum Reissner–Mindlin model. Furthermore, it is proved the first time that the recovered three-dimensional quantities exactly satisfy the continuity conditions on the interface between different layers and traction boundary conditions on the bottom and top surfaces. It is also shown that two of the equilibrium equations of three-dimensional elasticity can be satisfied asymptotically, and the third one can be satisfied approximately so that the difference between the Reissner–Mindlin model and the second-order asymptotical model can be minimized. Numerical examples are presented to compare with the exact solution as well as the classical lamination theory and the first-order shear-deformation theory, demonstrating that the present theory has an excellent agreement with the exact solution.     

Uniform asymptotics for finite-time ruin probability of a bidimensional risk model

Consider a continuous-time bidimensional risk model with constant force of interest in which the claim sizes from the same business are heavy-tailed and upper tail asymptotically independent. We investigate two cases: one is that the two claim-number processes are arbitrarily dependent, and the other is that the two corresponding claim inter-arrival times from different lines are positively quadrant dependent. Some uniformly asymptotic formulas for finite-time ruin probability are established.     

二阶渐近周期奇异哈密顿系统同宿轨道

运用集中紧性方法和Ekeland变分原理研究R^2中二阶渐近周期奇异Hamilton系统ue (1 g(t))V‘u(t,u)=0的极小问题，并证明该系统具有两条非平凡同宿轨道。     

Duality and Well Behavior of Nonconvex Functions

This article is devoted to the study of optimization problems involving a convex composite function, that is, the composition of a convex function with a mapping. We introduce the definitions of conjugate functions and associated subdifferentials which suit this particular structure. We use these definitions to study the conditioning, well-posedness, and well behavior of such functions.