Speaker: Wendi Wang, Key Laboratory of Eco-environments in Three Gorges Reservoir Region,
School of Mathematics and Statistics, Southwest University,
Chongqing, 400715, P. R. China
Title：Vegetation pattern formation of a
water-biomass model
Abstract: In this talk, I present a mathematical model with diffusion and cross-diffusion to describe
the interaction between the vegetation and the soil water. Based on the view of Turing
pattern, we discuss the conditions of the diffusion-induced instability and the cross-diffusion induced
instability of a homogenous uniform steady state. We find that either a fast diffusion
speed of water or a great hydraulic diffusivity due to the suction of roots may drive the
instability of the homogenous steady state. Furthermore, we find that both the rain-fall rate
and the infiltration feedback parameter can induce the transitions among the vegetation
state, pattern formation and bare soil state. It is also found that the “terrain slope” may
cause the instability of the homogenous steady state and drive the formation of periodic
stripe pattern. Consequently, the diversity of dryland vegetation in reality can be explained
as a result of pattern solutions of the model. The talk is based on the joint work with Xiaoli
Wang.
Time: 9:00-11:00pm, July 14th
Place: Room 316, Environmental Building, Renmin University
