Analysis of Resource Competition Models

Li0211614 该项目的目标是在资源竞争的背景下发展有关生物多样性的数学理论。最近的数值研究表明，对多种资源的竞争可以产生周期性振荡甚至混沌振荡，大量物种可以在非常有限的资源上共存。 然而，数学家和生态学家仍然缺乏对生态群落多样性产生机制的分析理解。 他研究了几种资源竞争模型，包括多资源的标准竞争模型和食物网内的竞争模型;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见解。 微分方程理论和动力系统理论被用来确定模型解的长期行为，表现为吸引定态、极限环或奇异吸引子。 重要的问题是什么原因导致竞争物种共存，并定位共存发生的参数范围。 在自然系统中维持物种多样性的问题长期以来一直吸引着数学家和生态学家。 这项工作提供了对影响丰度和生物多样性的因素的一般了解。 这些结果对于确定水生和陆生系统中物种组成的模式，以及管理森林和湖泊等自然资源具有重要意义。

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.