演講訊息 TALKS

In this talk, we consider a model of a flowing water habitat with a hydraulic storage zone in which no flow occurs. In this habitat, one or two microbial populations grow while consuming a single nutrient resource. Our model is a system of partial differential equations coupled with ordinary differential equations . Conditions for persistence of one population and coexistence of two competing populations are derived from eigenvalue problems, the theory of bifurcation and the theory of monotone dynamical systems. A single population persists if it can invade the trivial steady state of an empty habitat. Under some conditions, persistence occurs in the presence of a hydraulic storage zone when it would not in an otherwise equivalent flowing habitat without such a zone. Coexistence of two competing species occurs if each can invade the semi-trivial steady state established by the other species. We also answer an interesting question: Does a system with storage zones facilitate persistence of planktonic algae in flowing habitats? Numerical work shows that both coexistence and enhanced persistence due to a storage zone occur for biologically reasonable parameters.