Speaker: Pro.Zhicheng Wang（Lanzhou University）

Title: Monotonicity and Global Dynamics of a nonlocal two-species phytoplankton model

Time: Sat, Apr.27, 2019, AM:10:30-11:30

Location: Room 4318, Building No.4, Wushan Campus

Abstract:

       We investigate a nonlocal reaction-diffusion-advection system modeling the population dynamics of two competing phytoplankton species in a eutrophic environment, where nutrients are in abundance and the species are limited by light only for their metabolism. We first demonstrate that the system does not preserve the competitive order in the pointwise sense. Then we introduce a special cone $\mathcal{K}$ involving the cumulative distributions of the population densities, and a generalized notion of super- and subsolutions of \eqref{equ31}-\eqref{equ2} where the differential inequalities hold in the sense of the cone $\mathcal{K}$.  A comparison principle is then established for such super- and subsolutions, which implies the monotonicity of the semiflow with respect to the cone $\mathcal{K}$. As application, we study the global dynamics of the single species system and the competition system. The latter has implications for the evolution of movement for phytoplankton species. This is a joint work with Dr. Danhua Jiang, Prof. King-Yeung Lam, and Prof. Yuan Lou.