Traveling Wave Solutions in Nonlocal Dispersal Models With Nonlocal Delays

Abstract

Abstract. This paper is concerned with the traveling wave solutions of nonlocal dispersal models with nonlocal delays. The existence of traveling wave solutions is investigated by the upper and lower solutions, and the asymptotic behavior of traveling wave solutions is studied by the idea of contracting rectangles. To illustrate these results, a delayed competition model is considered by presenting the existence and nonexistence of traveling wave solutions, which completes and improves some known results. In particular, our conclusions can deal with the traveling wave solutions of evolutionary systems which admit large time delays reflecting intraspecific competition in population dynamics and leading to the failure of comparison principle in literature.

Minimal wave speed in a dispersal predator–prey system with delays

“…for any positive bounded continuous functions φ 1 (ξ ), ψ 1 (ξ ), φ 2 (ξ ), ξ ∈ R. Similar to Pan [24], Theorem 3.2, we can prove the following conclusions.…”