The existence of traveling wave solutions for a bistable three-component lattice dynamical system

We study the traveling wave solutions for a three-component lattice dynamical system. This problem arises in the modeling of three species competing two food resources in an environment with migration in which the habitat is one-dimensional and is divided into countable niches. We are concerned with the case when two species have different preferences of food and the third species has both preferences of food. To understand which species win the competition under the bistable condition, the existence of a traveling wave solution for this lattice dynamical system is proven.