Abstract
In this paper, we consider the asymptotic behavior and uniqueness of traveling wave fronts connecting two half-positive equilibria in a competitive recursion system. We first prove that these traveling wave fronts have the exponential decay rates at the minus/plus infinity, where for a given wave speed, there are three possible asymptotic behaviors for the first component of the wave profile at the plus infinity and the second component of the wave profile at the minus infinity, respectively. And then we use the sliding method to prove the uniqueness of traveling wave fronts for this system. Furthermore, by combining uniqueness and upper and lower solutions technique, we also give the exact decay rate of the weaker competitor under certain conditions.
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