具有生态位构建作用的种群进化动力学模型及其应用研究

依据进化动力学的理论与方法,系统探讨了生态位构建的机理与模式．通过建立生态位构建的空间模式及其适合度计算公式和具有生态位构建作用的单种群与两种群的进化动力学模型,并对其种群进化动态、种间竞争共存机制进行的理论与数值模拟分析,揭示了生物与环境资源的协同进化关系．结果表明:种群动态受其主要生态因子及资源含量的正反馈作用．生态位构建作用通过对种群适宜度的影响而产生进化响应．单种群动力系统存在种群大小的阈值效应;在两竞争种群动力系统中,生态位构建可以导致进化动力系统的多个竞争结果,从而为解释种间竞争与稳定共存提供了一种新的理论机制．     

生态环境系统中一类相互作用生态种群的动态优化与控制(英文)

生态环境系统是一个复杂的有待于综合运用生物科学、环境科学、信息科学、数学科学与计算机科学深入研究的信息系统.而其中对生态系统宏观优化调控决策的研究已成为了近年来国内、外数学与生态学工作者深入探讨的一大课题.基于当前生态种群研究须向宏观与微观两极纵深发展、延伸以及数量种群生态学复杂系统建模的需要,本文通过对一类具有竞争机理局部稳定的两种相互作用生态种群模型保解析性及其宏观优化调控的讨论,进一步将生态环境系统的调控严谨化,给一类生态系统的动态分析与调控优化提供了很有价值的方法与手段.这不仅对于两种相互竞争和互惠互存的生态系统的建模与分析具有重要意义,而且对于更为复杂的生态环境系统的动态分析与宏观调控也具有较大的指导作用与应用价值.     

多品牌经销商商品种群优化策略研究

为了平衡经销商对顾客个性化需求满足程度与商品维护复杂性和成本之间的矛盾,本文拓展生态学的生物种群理论和方法及应用范围,深入到企业的微观层面——商品,提出了商品种群的概念,构建出多商品种群动力模型以刻画了经销商商品族谱在竞争和协作环境中的演变机理,借鉴生态平衡理论评价经销商商品族谱稳定性和变化趋势。最后举例证明该方法的可行性和对经销商意义。     

企业竞争的进化博弈论与种群生态学模型

企业竞争与生物种群之间的生存竞争存在很大的相似性.根据企业竞争的特点,应用进化博弈论及种群生态学有关理论,推导并建立了企业竞争的生态学模型,并对其进行了深入分析,指出了企业竞争所产生的四种可能的均衡结果,最后说明企业竞争的过程实际上就是发现优秀企业和新的生产知识的过程.     

具脉冲效应的阶段结构单种群动力学模型

讨论了生物资源管理中的具脉冲出生与脉冲收获的单种群阶段结构动力学模型.利用离散动力系统频闪映射理论,得到了脉冲投放幼体对整个种群持续生存的重要意义.为现实的生物资源管理提供了可靠的策略依据,也丰富了脉冲微分方程理论.     

一类具年龄结构种群动力系统的最优控制

研究一类具年龄结构种群线性动力系统的最优控制问题 .由Mazur’s定理 ,我们证明了最优控制问题 (OH)最优解的存在性 ,同时借助于法锥概念 ,我们还得到了最优控制问题 (OH)最优解存在的必要条件     

具有时滞的种群动力系统模型中的特久性

本文通过构造持久性与绝灭性泛函去讨论具有时滞的种群动力系统模型中的持久性与非持久性。 作者在文中对二维的L-V系统,三维食物链与其它的具有时滞的系统给出了一些持久性与绝灭性泛函,从而也就判别了这些系统的持久性与非持久性。     

考虑污染和种内关系的种群扩散最优控制模型

针对污染和种内关系均影响细菌种群扩散这一管理生态学问题,本文建立了基于非线性拟抛物方程的最优控制模型,将外界环境向细菌种群输入的毒素率作为控制变量,运用控制理论和方法探讨污染和种内关系双重影响下种群扩散系统的最优控制问题。利用Schauder不动点定理证明了该种群扩散系统的适定性;同时,通过建立新的Carleman型估计,给出了容许控制和最优控制的存在性。最后,通过数值算例分析了理论推导的结果,在算例中都找到一对时间最优控制,验证了种群扩散系统最优控制模型的有效性。该研究结果对现代传染病预防具有借鉴意义,也为有效控制瘟疫的爆发和流行提供理论参考。     

年龄相关的种群扩散系统广义解的正则性

证明了年龄相关的种群扩散系统广义解的正则性,为进一步讨论该系统最优控制的存在性奠定了理论基础,也为种群系统控制问题的实际研究提供了数学理论和方法.     

一类具Rotenberg模型解的存在性

迁移方程是研究物质中的粒子运动所产生的微观效应综合所致的宏观迁移现象规律的一种模型,研究这类迁移方程对数学基础理论的发展有着非常重要的意义.在L_1空间中,运用线性算子理论,研究了种群细胞增生中具Rotenberg模型的迁移方程,采用所谓的豫解算子等法证明了种群细胞增生中具Rotenberg模型解的存在性.     

Bifurcation of spatially inhomogeneous auto-oscillations from a non-local homogeneous cycle in systems with small diffusion

The problem stated in the title is of interest both for theory and applications (e.g., in mathematical ecology). To solve this problem, the authors use the method of quasi-normal forms for constructing auto-oscillations in parabolic systems with small diffusion. Bibliography: 19 titles. To Olga Arsenievna Oleinik with best wishes on the occasion of her birthday This paper has been supported in part by the Russian Foundation for Basic Research. Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000.     

The stability of traveling waves with non-critical speeds for some competition systems

This paper is concerned with some quasilinear cross-diffusion systems which model competing species in mathematical ecology.By detailed spectral analysis,each traveling wave solution with non-critical speed is proved to be locally exponentially stable to perturbations in some exponentially weighted spaces.     

A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast-subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel–Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator–inhibitor switch from systems biology, a predator–prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel–Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator–inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator–prey model explosive population growth near a codimension-two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.     

Stabilization to a positive equilibrium for some reaction–diffusion systems

The aim of this paper is to study the asymptotic behavior of solutions for some reaction–diffusion systems in biology. First, we establish a Liouville type theorem for entire solutions of these reaction–diffusion systems. Based on this theorem, we derive the stabilization of the solutions of the reaction–diffusion system to the unique positive constant state, under the condition that this positive constant state is globally stable in the corresponding kinetic systems. Two specific examples about spreading phenomena from ecology and epidemiology are given to illustrate the application of this theory.     

Global stability of stationary solutions of reaction-diffusion systems

We give a condition which implies that the trivial solution, U ≡ 0, of a class of reaction-diffusion systems with homogeneous Dirichlet boundary conditions, is a global attractor for all nonnegative solutions. In certain cases, this condition, which relates the diffusion matrix and the domain to a parameter which depends on the nonlinear term, significantly improves similar conditions which can be obtained from energy estimates. Applications are given to equations arising in mathematical ecology.     

Existence of travelling waves with their minimal speed for a diffusing Lotka–Volterra system

Travelling waves are natural phenomena ubiquitously for reaction–diffusion systems in many scientific areas, such as in biophysics, population genetics, mathematical ecology, chemistry, chemical physics, and so on. It is pretty well understood for a diffusing Lotka–Volterra system that there exist travelling wave solutions which propagate from an equilibrium point to another one. In this paper, we prove there exists, at least, a wave front—the monotone travelling wave—with its minimal speed.     

Interdisciplinary education – a predator–prey model for developing a skill set in mathematics,biology and technology

The science of biology has been transforming dramatically and so the need for a stronger mathematical background for biology students has increased. Biological students reaching the senior or post-graduate level often come to realize that their mathematical background is insufficient. Similarly, students in a mathematics programme, interested in biological phenomena, find it difficult to master the complex systems encountered in biology. In short, the biologists do not have enough mathematics and the mathematicians are not being taught enough biology. The need for interdisciplinary curricula that includes disciplines such as biology, physical science, and mathematics is widely recognized, but has not been widely implemented. In this paper, it is suggested that students develop a skill set of ecology, mathematics and technology to encourage working across disciplinary boundaries. To illustrate such a skill set, a predator–prey model that contains self-limiting factors for both predator and prey is suggested. The general idea of dynamics, is introduced and students are encouraged to discover the applicability of this approach to more complex biological systems. The level of mathematics and technology required is not advanced; therefore, it is ideal for inclusion in a senior-level or introductory graduate-level course for students interested in mathematical biology.     

Applications of Category Theory to the Area of Algebraic Specification in Computer Science

The theory of algebraic specifications – one of the most important mathematical approaches to the specification of abstract data types and software systems – is reviewed from a mathematical and a computer science point of view. The important role of category theory in this area is discussed and it is shown how the following selected problems are treated using category theory: First, a unified framework for specification logics, second compositional semantics, third partial algebras and their specification, and fourth specifications and models for concurrent systems. For the solution of two of the problems classifying categories are used. They allow to present categories of algebras as functor categories and to derive a number of important properties from well known results for functor categories.     

基于因素空间理论的故障诊断数学模型及其应用

本文利用汪培庄教授提出的因素空间理论,为诊断问题下了一个新的数学定义,以此为基础,给出了故障诊断的数学模型。最后讨论了故障诊断专家系统的构建方法及其应用。     

The algebra of marriage: an episode in applied group theory

In 1949, André Weil contributed a mathematical appendix to Claude Lévi-Strauss's landmark book, The elementary structures of kinship. In this appendix, Weil (one of the Bourbaki mathematicians) used group-theoretic techniques to model Australian marriage systems. Weil's paper marked the beginning of mathematical anthropology. This essay describes Weil's analysis of marriage systems and traces the uneasy history of the application of group theory to kinship studies.