一类慢变Filippov捕食-被捕食系统的分岔机理分析

研究了生态学中含控制策略项的一类Filippov捕食-被捕食系统,由于害虫的环境容纳量受外界环境因素的影响而变化,故将害虫的环境容纳量视为周期慢变量,当慢变量的频率与系统的固有频率存在量级差异时,使得该Filippov捕食-被捕食系统体现出两时间尺度效应.通过将周期演变的环境容纳量视为控制参数,针对相应的广义自治系统,进行了平衡点的稳定性与分岔分析.借助于快慢分析法、微分包含理论,得到了在典型参数条件下,系统展现的一些特殊分岔模式,并对相关的机理予以了解释,由此丰富了对该类Filippov捕食-被捕食系统的研究.     

一类具有分段常数变量的三维食饵捕食者系统的稳定性和分支行为

本文研究一类具有分段常数变量的三维食饵-捕食者系统的稳定性和分支行为,该系统由一个捕食者和两个食饵构成,其中一个食饵可由捕食者对另一个食饵的捕食行为中获益.首先通过计算得到三维食饵-捕食者系统对应的差分模型,其次通过选择合适的参数讨论边界和正平衡点的存在性,进而利用线性稳定性理论讨论平衡点局部渐近稳定的充分条件.将两个食饵种群的出生率以及最大环境容纳量作为分支参数,使用分支理论研究差分模型在平衡点处产生翻转分支、Neimark-Sacker分支、折-翻转分支和1:2共振分支的充分条件.最后通过数值模拟验证了理论分析的正确性.     

捕食者环境容纳量依赖于食饵的食饵-捕食者模型

本文建立捕食者环境容纳量依赖于食饵数量的食饵-捕食者模型,分析了模型解的全局性态.可能同时存在多个正平衡点,它们当中会有鞍点或鞍结点.除鞍点外每个正平衡点都有一个吸引域.高寒草甸植被与高原鼠兔之间的关系可以用所建立的模型来描述,利用模型参数的实际值分析了高寒草甸退化的原因和恢复策略.过度放牧、人类不合理活动的加剧、高原鼠兔天敌的减少都是高寒草甸退化的原因.相应地,通过合理放牧、规范人类活动、保护或招引高原鼠兔的天敌、药物控制可以恢复退化的高寒草甸.     

一个具有时滞和阶段结构的捕食-被捕食模型

研究一个具有时滞和阶段结构的捕食者-食饵模型.通过构造适当的Lyapunov泛函,讨论了该模型的正平衡点和非负边界平衡点的全局吸引性,从而得到了保证该生态系统永久持续生存与绝灭的充分性条件.     

棉田生态系统时滞动力学模型及其应用

以棉田生态系统能量流动分析为基础,建立了作物-害虫-天敌-微生物的时滞种群动力学模型,利用泛函微分方程理论对该系统进行了持久性和稳定性研究,对系统解的正性、持久性、正平衡点的存在性及全局渐近稳定性给出了相关条件,证明该系统的时滞是无害时滞.最后使用MATLAB软件对模型进行了动态模拟,对正平衡点的存在性条件和稳定性进行了验证.     

近岸海域赤潮藻非线性生态模型的建立和动力学分析

基于海洋浮游生态系统特性,以主要赤潮藻-中肋骨条藻为研究对象,建立了中肋骨条藻生物量随氮磷营养盐浓度变化的微分方程,并考虑了养料循环和时滞的影响,利用非线性动力学方法得到了边界平衡点的全局渐近稳定性,正平衡点的局部稳定性和Hopf分支的存在性,以及系统持久的充分条件.     

害虫胁迫下的棉田能量生态系统稳定性分析

在棉田生态系统的基础上研究了以能量为单位的能流数学模型,模型主要包括五个种群:棉株、害虫、捕食性天敌、寄生性天敌以及土壤微生物.基于模型使用微分方程模拟出了能量在各个每个物种之间的流动,并给出了系统的正平衡点存在性和稳定性的条件.最后使用Matlab软件对模型中各个种群的能量变化进行直观的模拟.旨在通过已知的模型在正平衡点处稳定的条件,对棉田生态系统的管理和系统控制提供理论指导.     

作物害虫天敌微生物系统的动力学研究

以棉田生态系统能量流动分析为基础,建立了作物害虫天敌微生物的种群动力学模型,对作物害虫天敌微生物系统进行了初步的研究.对系统的能量流动使用微分方程进行了模拟,并对系统正平衡点的存在性及局部渐近稳定性给出了相关条件.最后使用MATLAB软件对模型进行了动态模拟,对正平衡点的存在性条件和稳定性进行了验证.     

一类具有时滞的捕食者-猎物-共生者系统的研究

该文建立了具有时滞的捕食者-猎物-共生者系统模型,对模型的正性,持久性和局部稳定性记性了分析.得出此系统具有稳定的可能,正平衡点也具有渐近稳定的可能.最后用棉蚜生态系统中的瓢虫、棉蚜、蚂蚁的相关数据进行数值模拟,得出猎物和捕食者的发育历期(时滞)对整个系统具有重要影响,若发育历期过长,则整个系统将具有周期性的波动.     

具有时滞的生态流行病模型的稳定性和Hopf分支

该文考虑一类食饵染病的时滞捕食被捕食模型. 作者分析了系统的非负不变性, 边界平衡点的性质和全局稳定性. 证明了当时滞τ=τ\-1+τ\-2适当小时, 正平衡点是局部渐近稳定的,随着时滞的增加, 正平衡点由稳定变为不稳定, 系统在正平衡点附近发生Hopf分支.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

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An alternative mathematical algorithm for the photo- and videokeratoscope

Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography.