We study the stability and uniqueness of nonzero speed traveling waves for a three-component lattice dynamical system. This system arises in the study of three species competition model in which there is no competition between the first and the third species. Under the bistable consideration, we first derive the strict monotonicity of nonzero speed traveling waves. Then some super-sub-solutions are constructed based on these strictly monotone traveling waves. Finally, utilizing the constructed super-sub-solutions, we prove the stability and uniqueness of nonzero speed traveling waves of this system.
Journal of Mathematical Analysis and Applications 472(2), p.1534–1550