Analysis Of Dynamic Behavior Of Zooplankton And Algae In Flowing Habitats

In the lake ecology, there is complex and diverse interaction between plankton species. This phe-nomenon not only affects the dynamic changes and succession of the lake species, but also influences on the change of lake environment.This paper mainly studies the dynamics of zooplankton and algae in flowing habitats through reaction-diffusion-advection model. The main channel in the flowing habitats is connected with the hydraulic storage zone. No diffusion and advection happen in the hydraulic storage zone.This paper is divided into three parts. The first part is the introduction of background, and the sec-ond part studies the food chain model of single nutrient, single algae and single zooplankton.By using the conservation principle, maximum principle and semigroup theory, the paper studies the well-posedness of solution of the system. In order to analyze the permanence of the system, this paper defines the basic repro-duction number of the algae and zooplankton, that is Ro and Rz,meaning the net reproductive rate of algae and zooplankton. By using eigevalue problems and persistence theory, we get the following conclusion: When Ro<1, zooplankton and algae will become extinct.When R0>1,Rz>1, there exists coexistence steady state and the zooplankton is uniformly persistent.The third part deals with a model of single nutrient, single algae and two zooplankton species.Similarly, we get the well-posedness of the solution of the system, and define the basic reproduction number Rc.WhenR0<1> two zooplankton species and algae will. When R0>1.Rz>1.Rc>1, two zooplankton species and algae will coexist.