Analysis of Resource Competition Models

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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.