Abstract
We consider a three components lattice dynamical system which arises in the study of a three species competition model. It is assumed that two weaker species have different preferences of food and the third stronger competitor has both preferences of food. Under this assumption, it is well-known that there is the minimal speed such that a traveling wave solution exists for any speed above this minimal one. In this paper, we prove the monotonicity of wave profiles and the uniqueness (up to translations) of wave profiles for each given admissible speed under certain restrictions on parameters.
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