Almost periodic traveling waves for a nonlocal dispersal system

Abstract

This paper mainly deals with the monotonicity, stability, uniqueness and existence for almost periodic traveling waves to a nonlocal dispersal system. The difference from some previous works is mainly reflected in diffusion terms. First, the comparison principle of nonlocal diffusion equations is built by the contradiction method and some analysis techniques. Moreover, the difficulty of establishing the monotonicity to almost periodic traveling waves for the emergence of system is solved by introducing the standard partial ordering in matrices and some analysis techniques. Therefore, the results for the stability and existence for periodic traveling waves to nonlocal diffusion equations are extended to almost periodic systems, and those conclusions related to almost periodic traveling waves for scalar equations with Laplace diffusion are generalized to nonlocal diffusion systems.