Dynamics of a Three Species Competition Model
Discrete and Continuous Dynamical Systems-A
We investigate the dynamics of a three species competition model, in which all species have the same population dynamics but distinct dispersal strategies. Gejji et al.  introduced a general dispersal strategy for two species, termed as an ideal free pair in this paper, which can result in the ideal free distributions of two competing species at equilibrium. We show that if one of the three species adopts a dispersal strategy which produces the ideal free distribution, then none of the other two species can persist if they do not form an ideal free pair. We also show that if two species form an ideal free pair, then the third species in general can not invade. When none of the three species is adopting a dispersal strategy which can produce the ideal free distribution, we find some class of resource functions such that three species competing for the same resource can be ecologically permanent by using distinct dispersal strategies.
Lou, Yuan and Munther, Daniel, "Dynamics of a Three Species Competition Model" (2012). Mathematics Faculty Publications. 259.