Analysis of Resource Competition Models

资源竞争模型分析

基本信息

批准号：
0211614
负责人：
Bingtuan Li
金额：
$ 7.54万
依托单位：
University of Louisville Research Foundation Inc
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2002
资助国家：
美国
起止时间：
2002-09-01 至 2006-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0211614&HistoricalAwards=false
关键词：
Analysis Resource Competition Models

项目摘要

Li0211614 The goal of this project is to develop mathematical theoryregarding biodiversity in the context of resource competition.Recent numerical work suggests that competition for multipleresources can generate periodic oscillations or even chaoticoscillations, and a large number of species can coexist on veryfew limiting resources. However, both mathematicians andecologists still lack analytic understanding of mechanisms thatgenerate diversity in ecological communities. The investigatorstudies several resource competition models, including standardcompetition models with multiple resources and competition modelswithin food webs; he gives rigorous analysis for the models andprovides insight into diversity of competing species. Theory ofdifferential equations and theory of dynamical systems are usedto determine the long-term behavior of solutions of the models inthe form of attracting steady states, limiting cycles or strangeattractors. Important issues are what causes competing species tocoexist, and locating parameter ranges in which coexistenceoccurs. The question of the maintenance of species diversity innatural systems has intrigued mathematicians and ecologists for avery long time. This work provides a general understanding offactors affecting abundance and biodiversity. The results haveimportant implications for determining the patterns of speciescomposition in aquatic and terrestrial systems, and for managingnatural resources such as forests and lakes.

LI0211614该项目的目的是在资源竞争的背景下发展数学理论，将生物多样性授权。当时的数值工作表明，对多个多工具的竞争可以产生定期的振荡甚至混乱，并且大量物种可以在非常限制的资源上共存。但是，数学家和生物学家仍然缺乏对生态社区多样性的机制的分析理解。研究人员研究了几种资源竞争模型，包括具有多种资源和竞争模型的食品网的标准竞争模型；他对模型进行了严格的分析，并提供了对竞争物种多样性的洞察力。使用差异方程的理论和动力学系统理论来确定模型解决方案的长期行为，以吸引稳态，限制周期或strenteateattractors的形式。重要的问题是导致竞争物种托妥诊断的原因，并定位共存的参数范围。维持物种多样性内在系统的问题使数学家和生态学家很长时间以来就吸引了数学家和生态学家。这项工作提供了影响丰度和生物多样性的一般理解。结果对确定水生和陆地系统中的物种序列的模式以及管理森林和湖泊等资源具有重要意义。