Existence and stability of traveling wavefronts for a nonlocal delay Belousov–Zhabotinskii system

Abstract

This paper is concerned with the existence and stability of traveling wavefronts for a nonlocal delay Belousov–Zhabotinskii system. We first introduce the new variable and change the two-dimensional system with nonlocal delay into a three-dimensional system without delay. Then the existence of traveling wavefronts is obtained by constructing a pair of suitable super- and sub-solutions and applying Schauder's fixed point theorem. Finally, we establish the exponential stability of traveling wavefronts with large speed by the weighted energy method together with the comparison principle, when the initial perturbation around the traveling wavefront decays exponentially as , but can be arbitrarily large in other locations.