Talk 1: Population models with Allee effect in Advective Environment

Time/location:  May 21,  4:00-5:00pm, 中国人民大学环境楼316 

Abstract: We show that in a spatial population model with strong Allee effect, the population becomes extinct no matter how large the initial population is, if the advection is strong enough. Hence the extinction equilibrium is globally asymptotically stable, which is quite different from the case of small or no advectionthat the dynamics is bistable. We will show results in both ODE patch model and reaction-diffusion-advectionmodel. It is based on joint work with Leah Shaw, Maggie Swift, Yan Wang (College of William and Mary), and Jinfeng Wang (Harbin Normal University).


Talk 2: Coexistence of competing species for intermediate dispersal rates in a reaction-diffusion chemostat model 

Time:  May 22, 4:00-5:00pm,  中国人民大学环境楼316

Abstract: We revisit a classical reaction-diffusion chemostat model with two species of bacteria. From the monotone dynamical system, it is know that the two species can coexist if some spectral conditions are satisfied, but such conditions are difficult to verify. We prove that the coexistence can be achieved when the diffusion rates are in an intermediate range, which partially confirms some conjecture by theoretical ecologists. This is a joint work with Yixiang Wu (Vanderbilt University) and Xingfu Zou (University of Western Ontario).