一类具有随机周期移民扰动的非线性人口发展方程随机周期解的存在唯一性

本文给出了一类具有随机周期移民扰动的非线性m增生人口发展方程随机周期解的存在性和唯一性结论。     

非线性奇摄动人口问题的渐近解

研究了一个非线奇摄动人口问题、在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量和幂级数展开理论构造出解的形式渐近展开式．最后利用微分不等式理论,讨论了问题解的一致有效性．     

人口问题中具广义Ginzbur-Landau型方程解的渐近性和Blow-up

在文献[1][2][3]和[4]的基础上,研究人口问题中具广义Ginzbur-Landau型弥散方程（0.21）,（0.22）及更一般的非线性高阶抛物型方程（0.23）初边值问题,在古典解存在且唯一的条件下,利用文[7,8]的相应方法,深入探讨问题的广义解和古典解的渐近性及Blow-up现象,得到许多新结果。     

具势能衰减的非线性拟抛物方程整体解的不存在性

利用Laplace算子的特征函数法研究了一类具势能衰减的非线性拟抛物方程的初边值问题整体解的不存在性与有限时间爆破．     

Forcing Function Diagnostics for Nonlinear Dynamics

Summary .  This article investigates the problem of model diagnostics for systems described by nonlinear ordinary differential equations (ODEs). I propose modeling lack of fit as a time-varying correction to the right-hand side of a proposed differential equation. This correction can be described as being a set of additive forcing functions, estimated from data. Representing lack of fit in this manner allows us to graphically investigate model inadequacies and to suggest model improvements. I derive lack-of-fit tests based on estimated forcing functions. Model building in partially observed systems of ODEs is particularly difficult and I consider the problem of identification of forcing functions in these systems. The methods are illustrated with examples from computational neuroscience.     

一类高阶非线性中立型时滞差分方程正解的存在性定理

研究了一类高阶非线性中立型时滞差分方程正解的存在性,给出了该类方程存在有界最终正解的一个充要条件。     

Nonlinear Analysis of the Dynamics of DNA Breathing

The base pairs that encode the genetic information in DNA show large amplitude localized excitations called DNA breathing. We discuss the experimental observations of this phenomenon and its theoretical analysis. Starting from a model introduced to study the thermal denaturation of DNA, we show that it can qualitatively describe DNA breathing but is quantitatively not satisfactory. We show how the model can be modified to be quantitatively correct. This defines a nonlinear lattice model, which is interesting in itself because it has nonlinear localized excitations, forming a new class of discrete breather.     

具Sobolev-Galpern型湿气迁移方程解的渐近性和Blow-up

本文在文献[1,2,3,4,6]的基础上,对具有Sobolev-Galpern型土壤中湿气迁移方程和更一般的非线性拟抛物物型方程的初边值问题,在其解存在唯一的条件下,利用文献[5,7]的方法,深入探讨了相应问题解决的渐近性和爆破现象,得到了许多新结果。     

一类具年龄结构的线性周期种群动力系统的最优控制

研究一类具有年龄结构的线性周期种群线性动力系统的最优控制问题,即讨论了具有周期的生死率和周期变化的控制项的模型．利用Mazur's定理,证明了最优控制问题最优解的存在性,同时由法锥概念的特征刻画,我们还得到了最优控制问题最优解存在的必要条件．     

格氏栲种群数量动态的谱分析研究

运用谱分析数学方法,研究分析格氏栲林格氏栲种群动态规律．结果表明：格氏栲种群数量动态的周期波动性是明显的,与格氏栲天然更新过程有关;不同生境、人为干扰均对辂氏栲种群数量动态的波动产生影响;格氏栲生长量的周期波动与其种群数量动态的周期波动特征基本一致,表明格氏栲种群数量动态呈周期波浪式发展,即表征格氏栲林优势种群的稳定性。