Abstract
In this paper, we investigate the invading speeds for a three-species competition system. By deriving the existence and non-existence of a class of traveling waves connecting two different constant equilibria of this competition system, we characterize the minimal invading speeds of two alien species in the case of one single weak aboriginal species and of a single alien species in the case of two weak aboriginal species, respectively. Moreover, depending on different conditions on the parameters of this competition system, we show that either a strong alien competing species can wipe out the other two species; or three weak competing species can live together.
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