Threshold dynamics of a periodic parabolic system modeling the influence of salinity and nutrient recycling on the growth of algae
Feng-Bin Wang
Department of Natural Science Center for General Education
Chang Gung University
fbwang@mail.cgu.edu.tw, fbwang0229@gmail.com
In this talk, we shall study a periodic advection-dispersion-reaction system incorporating the effects of salinity, nutrient recycling, temperature, and spatial variations for the growth of harmful algae in riverine ecosystems. We can introduce the basic reproduction number `R_0` for algae and show that `R_0` serves as a threshold value for persistence and extinction of the algae. More precisely, we prove that the washout state is globally attractive if `R_0<1`, while there exists a positive periodic state and the algae is uniformly persistent if `R_0>1`. This talk is based on ongoing projects joint with Drs. James P. Grover and Xiao-Qiang Zhao.Keyword: harmful algae, salinity, nutrient recycling, the basic reproduction number