Abstract
This dissertation consists of chapter 1-3. Chapter 1-2 treat of applications of the chemostat to model the coexistence and competition for species with internal storage in the partially-mixed environment, while Chapter 3 is concerned with species in flowing habitats with a hydraulic storage zone. The problem of understanding competition for resources in spatially variable habitats is a challenging and very significant one for theoretical ecology. The specific question of how storage of nutrient resources affects competition in spatially variable habitats is virtually unknown from a theoretical perspective. Recently Grover used a Lagrangian modeling approach to study the competition of phytoplankton for a single nutrient resource. Each competitor population is divided into many subpopulations that move through two model habitats with gradient in nutrient availability: an unstirred chemostat and a partially-mixed water column. By numerical simulations, he concludes that the competitive exclusion holds. However his mathematical model can not be formally formulated and his results are numerical, not analytic. In Chapter 1-2, we construct two systems of reaction-diffusion equations to describe the coexistence and competition for species with internal storage in an unstirred chemostat. In Chapter 3, we introduce more realistic spatial models – riverine reservoir with hydraulic “storage zones”. The flow reactor model has similar boundary flows as in the unstirred chemostat, but with advective transport in addition to diffusion. Motivated by considering habitats such as broad high-order rivers or riverine reservoirs constructed by damming a river, we introduce a modification of the flow reactor model. Storage zones were originally introduced in hydraulic models to accurately describe transport of nonreactive tracers. Here we introduce a storage zone model for phytoplankton growing both in the flowing zone and the storage zone and derive conditions for persistence of a single species and coexistence of two competing species. In this dissertation we used the following arguments: Monotone dynamical system, Theory of bifurcation, Degree theory, upper-lower solution, Maximum principle。