Forced waves and gap formations for a Lotka-Volterra competition model with nonlocal dispersal and shifting habitats

This paper is mainly concerned with the forced waves and gap formations for a Lotka-Volterra competition model with nonlocal dispersal and shifting habitats. We first show that there exist two positive numbers c(1)* and c(2)* such that the system admits a forced wave provided that the forcing speed c is an element of (-c(2)*, c(1)*) by the iterative techniques combining with some known results for the forced moving KPP equations. Meanwhile, we use some delicate analysis to obtain the asymptotic behaviors at infinity of the forced waves with nonzero forcing speed c is an element of (-c(2)*, 0) boolean OR (0, c(1)*). Then, based on the comparison argument, we prove that the gap formations exist for c > c(1)* and c < -c(2)*. Finally, some numeric simulation results are presented to confirm our theoretical results, which also contains the critical cases of c = c(1)* and c = -c(2)*. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates forced waves and gap formations for a Lotka-Volterra competition model with nonlocal dispersal and shifting habitats. Through iterative techniques, the existence of forced waves is shown, and asymptotic behaviors at infinity are obtained through delicate analysis. The presence of gap formations is proven through comparison arguments for certain ranges of forcing speeds.