Limiting Profiles of Lotka-Volterra Competition-diffusion System with Large Advection in Three Species Dynamics

• Main Authors: Tien-fu Yu, 游天福
• Other Authors: Jann-long Chen
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/26042259835029050619

碩士 === 國立中央大學 === 數學研究所 === 99 === In this thesis, we first consider a Lotka-Volterra competition-diffusion-advection model for two competing species in a heterogeneous environment. The two species are identical except for their dispersal strategies: One is just random diffusion while the other is "smarter"- a combination of random diffusion and a directed movement up the environmental gradient. In [3], Chen and Lou conjectured that if the environment function $m$ has multiple local maxima, then the "smarter" species must concentrate at all local maximum of m. Nevertheless, in [6], Lam and Ni found that the "smarter" species will die out if the local maximum of m is smaller than the density of the other species. In this article, we consider a model of three species and expect that the related results will be similar to those in [6].