Mathematical Sciences: Mathematical Models in Microbial Ecology

在这个项目中，研究将集中在差分 方程模型研究空间异质性的影响， 微生物生长的间接营养消耗。 模型 两个竞争种群的方程产生强单调 动态系统，稳定状态共存已被证明， 是可能的。 利用非线性分析中的各种技术， 数值模拟，研究人员将研究选择 共存的参数，微生物流动性对 最大数量的共存物种。 对间接营养素消耗的研究将侧重于以下模型： 营养物质的细胞外和细胞内转化 转化为一种中间产物，被同化用于生长。 的 目标是比较不同消费的效率 过程，并研究物种共存的可能性 不同的营养吸收机制。 这个项目是关于数学的研究 连续培养中微生物生长和竞争的模型， 微生物学中常用的实验室技术。 微生物在自然生态中起着非常重要的作用 系统，他们的活动有许多工业 应用，例如，废水处理，食品生产， 药物和各种其他化学品、细菌控制等。 不同物种之间的竞争是一个重要的特征， 许多生态系统和许多工业设计 处理，例如，生物制剂在细菌控制中的应用， 废物处理，是基于不同的竞争力 物种 微生物活性的实验研究 实验室环境特别适合数学 用微分方程建模。 模型分析 方程可以更好地理解基本原理 微生物的行为，并经常导致新的实验 的设计.

In this project research will be focused on differential equation models studying the effects of spatial heterogeneity and indirect nutrient consumption on microbial growth. The model equations for two competing species generate a strongly monotone dynamical system, and steady state coexistence has been shown to be possible. Using various techniques in nonlinear analysis and numerical simulations, the investigator will study the choice of parameters for coexistence, the effect of microbial mobility on coexistence, and the maximum number of coexisting species. Research on indirect nutrient consumption will focus on models of both extracellular and intracellular conversion of the nutrient to an intermediate product which is assimilated for growth. The goal is to compare the efficiency of the different consumption processes, and to study the possibility of coexistence of species with different mechanisms of nutrient assimilation. This project is concerned with the study of mathematical models of microbial growth and competition in continuous culture, a commonly used laboratory technique in microbiology. Microorganisms play very important roles in natural ecological systems, and their activities have numerous industrial applications, e.g., waste water treatment, production of food, drugs and various other chemicals, bacterial control, etc. Competition between different species is an important feature in many ecological systems, and the design of many industrial processes, e.g., use of biological agents in bacterial control or waste disposal, is based on the competitiveness of different species. Experimental study of microbial activities in laboratory environments are especially amenable to mathe matical modeling by differential equations. Analysis of the model equations gives better understanding of the underlying principles of microbial behaviors, and often leads to new experimental designs.