脉冲输入毒素对具有阶段结构的单种群生存影响的研究

研究了一类小容量污染环境中脉冲输入毒素对具有阶段结构的单种群生存问题,分别找到了种群生存与灭绝的阈值,利用不等式放缩技巧,得到了种群灭绝和持久生存的充分条件.利用MATLAB数值仿真,验证了理论结果的正确性,分析了毒素输入量,毒素输入周期及种群成长时间对种群生存的影响.     

基于年龄结构的种群系统的最优收获控制

研究一类带年龄结构的非线性种群系统的最优收获问题.建立单种群阶段结构模型,对成年、幼年种群同时捕获,得到了单种群阶段结构模型在正平衡点渐近稳定的充分条件;并给出了脉冲控制时间间隔的上界估计值.分别对其幼年种群和成年种群捕获问题,给出以最大捕获可持续均衡收获(M SY)为目标的最优捕获策略.     

一类食物链模型的全局定性分析

文系统地研究了由一个食饵种群和两个捕食者种群所构成的食物链系统.结论表明：种群间的相互作用可以导致两个捕食者种群灭绝或一个捕食者种群灭绝,或者所有三个种群能以稳定的正平衡态或振动解的形式共存.利用MATLAB软件,该文提供了两个例子来模拟这些结论.     

一类捕食者具有阶段结构的捕食——被捕食模型的全局性态分析

在假设捕食的受益是减少死亡下,建立了一类捕食种群具有阶段结构的捕食-被捕食模型,分析得到了不存在食饵种群情形下捕食者种群模型和食饵存在时捕食-被捕食模型的平衡点存在性和全局稳定性,并确定了决定模型动力学性态的捕食者种群基本再生数、捕食存在时的食饵种群净增长率以及食饵灭绝与否的捕食率阈值.     

污染环境中的非自治种群模型的生存分析

研究了环境污染对种群的长期影响.考虑到新生个体的出生对种群体内毒素的影响,以及死亡的种群个体将体内毒素带回环境,建立了一个非自治数学模型.主要运用比较定理得到了种群一致持续生存、弱持续生存以及绝灭的判据.     

创新企业种群成长动力学分析

以生物系统中种群动力学为主要理论依据,开发了创新种群成长动力学模型.方程组推导结果表明:创新种群的成长过程中存在一定的均衡条件.科研种群是创新创群的主要互动种群.创新种群和科研种群之间存在显著地激励机制,两类种群对创新资源的占用存在一定的比例关系.创新种群的增长收到多种环境因素的影响,政府部门、服务机构、科研种群的影响均不同.创新种群的总量平衡点受总体环境制约.创新种群的增量平衡点主要受科研种群影响.     

具有HollingⅡ型功能反应和Allee效应的捕食系统模型

利用计算机模拟方法研究一类离散种群相互作用模型的动态复杂性.通过理论推导建立食饵具有Allee效应和HollingⅡ型功能反应的自治捕食系统模型,用Matlab软件模拟离散种群的生长状态,探索研究参数的变化对种群大小的影响,阐释Allee效应及HollingⅡ型功能反应在种群间相互作用模型中的重要性.研究结果表明:1)当处理时间处于有效区间内时,处理时间越大种群的稳定共存参数域越大;2)Allee效应的引入使种群的动态行为更为复杂,从而增加了捕食者种群的灭绝风险;3)系统受强Allee效应的影响,种群会出现提前分叉现象,如果继续增加Allee效应就会导致种群灭绝;4)强Allee效应更容易使种群趋向灭绝.所得结论在丰富生态学理论的同时,提出了保护生态学的重要依据.     

周期竞争Lotka-Volterra系统的持久性和灭绝性

研究周期竞争Lotka-Volterra系统,改进了两种群竞争排斥的充分条件,并且把竞争排斥原理推广到多种群的情形,给出了多种群系统中种群持久和灭绝的充分条件.     

求解约束优化问题的一种算法的改进

针对用遗传算法求解约束优化问题时,初始种群产生的方法进行了研究,提出了初始种群产生的一种新方法.实验证明,该方法较直接利用随机数产生初始种群的方法,具有更快的运算速度.     

一类污染环境下具有脉冲输入的竞争培养模型的定性分析

本文研究了污染环境下具有脉冲输入的竞争培养模型.利用乘子理论和小振幅扰动法,我们得到了种群灭绝周期解全局渐近稳定的充分条件,同时还得到了种群持久的条件.我们的结果表明环境污染能最终导致种群灭绝.     

A mathematical-model approach to human population explosions caused by migration

If the human population density becomes extremely high in a small area, then we say that a population explosion occurs in the area. Geographical movements of human population can form a regional overconcentration of population. If such an overconcentration becomes excessive, then it often forms a population explosion. In this paper, by taking a mathematical-model approach to human population explosions caused by migration, we obtain a sufficient condition for population to explode. It is known in sociodynamics that geographical population movements are described by a nonlinear integro-partial differential equation whose unknown function denotes the population density. This equation is called the master equation, and has its origin in statistical physics. We express a population explosion as a blow-up solution to the initial-value problem for this equation. We will study a population explosion as an interdisciplinary subject among human population dynamics, statistical physics, and the theory of nonlinear functional equations. The principal result is as follows: if a human population migrates within a sufficiently small domain, if the gradient of initial population density is sufficiently large, if the population gravitates strongly toward densely populated areas, and if a cost incurred in moving is sufficiently small, then a population explosion occurs.     

Does movement toward better environments always benefit a population?

We study the effects of advection along environmental gradients on logistic reaction-diffusion models for population growth. The local population growth rate is assumed to be spatially inhomogeneous, and the advection is taken to be a multiple of the gradient of the local population growth rate. It is also assumed that the boundary acts as a reflecting barrier to the population. We show that the effects of such advection depend crucially on the shape of the habitat of the population: if the habitat is convex, the movement in the direction of the gradient of the growth rate is always beneficial to the population, while such advection could be harmful for certain non-convex habitats.     

离散状态方程在人口预测问题中的应用

应用地域状态变量建立了人口发展的离散模型.一个重要目的就是评价中国的城市化和人口政策产生的影响.这些问题包括人口数量的预测和关于一些人口指标的讨论,如:人口地域分布、人口年龄分布、性别比、老龄化、抚养率,等.进而讨论了应在何时采取怎样的政策来应对未来的人口困境.     

人口迁移模型的改进及系统动力学仿真预测

求出了Keyfitz模型和Rogers模型的理论解,并以Rogers模型为例,对人口迁移模型进行了改进,使之适用范围更广.在人口迁移模型的基础上,建立了系统动力学模型,并对江西省的人口迁移问题进行了仿真预测,模拟出了江西省农村人口、城镇人口及城市化率的变化趋势.     

Parasite population dynamics within a dynamic host population

Summary We propose a stochastic process model for a parasite population living within a host population. The host population is described by an immigration-death process. The parasite population in one host is an immigration-birth-death-emigration process. The death of all parasites at the moment of death of their host is regarded as emigration. We derive explicit expressions for the distributions of the size of the host population, of the parasite load of one host individual and of the parasite population in the total host population and obtain conditions for the existence of limiting distributions if time is tending to infinity. For particular lifetime distributions of hosts including parasite induced mortality and heterogeneous infection risk we finally derive properties of the limiting distributions.Dedicated to Klaus Krickeberg on the occasion of his 60th birthday     

Extinction and blow-up phenomena in a non-linear gender structured population model

In this article we consider a gender structured model in population dynamics. We assume that the fertility rate depends upon the weighted population of males instead of total population of males. The proportion of males in the population is determined by fixed environmental or social conditions. Here we prove an existence and uniqueness result for a non-trivial steady state. If the initial age distribution is uniformly below the non-trivial steady state then we show that the total population goes extinct in infinite time. On the other hand, if we take the initial age distribution to be uniformly above the steady state then the total population blows up exponentially with time.     

Modelling the depletion of forestry resources by population and population pressure augmented industrialization

In this paper, a nonlinear mathematical model is proposed and analysed to study the depletion of forestry resources caused by population and population pressure augmented industrialization. It is shown that the equilibrium density of resource biomass decreases as the equilibrium densities of population and industrialization increase. It is found that even if the growth of population (whether intrinsic or by migration) is only partially dependent on resource, still the resource biomass is doomed to extinction due to large population pressure augmented industrialization. It is noted that for sustained industrialization, control measures on its growth are required to maintain the ecological stability.     

基于成分统计的我国人口年龄构成变动分析

人口年龄构成是总人口自然素质的重要表现因素,它不仅关系到人口自身的发展问题,同时也会对社会经济发展产生重大的影响。本文根据1990-2006期间的人口分性别年龄普查和抽样调查资料,对这一时期我国人口年龄构成及其变动情况进行了分析。主要内容包括:男性人口年龄构成变动的描述性分析,女性人口年龄构成变动的描述性分析,男性人口年龄构成与女性人口年龄构成的对比和检验等。     

基于GWR模型的河南省人口分布的影响因素研究

近年来,人口作为一种基本信息已成为目前研究的热点问题之一.人口分布可能受自然,经济,社会,政治等诸多因素的影响.因此,人口分布的研究对于了解不同类型区域的人口资源与经济发展之间的关系,因地制宜地发展本地经济具有重大意义.课题以河南省统计年鉴数据为基础,研究河南省人口分布的影响因素.具体来说,首先利用Surfer软件的可视化技术研究了河南省人口数量的空间变化特征.其次,利用近年来发展起来的地理加权回归模型对河南省人口分布的影响因素进行了定量分析.通过上述分析提取有效信息,从而为制定合理的人口政策和实现人口的有序流动提供必要的理论支持.