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

• Published in: Nonlinear analysis: real world applications Vol. 58; p. 103208
• Main Authors: Wang, Jia-Bing, Wu, Chufen
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2021
• Subjects: Forced waves; Gap formations; Lotka–Volterra competition model; Nonlocal dispersal; Shifting habitats; Forced waves; Shifting habitats; Lotka–Volterra competition model; Gap formations; Nonlocal dispersal
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2020.103208

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 c1∗ and c2∗ such that the system admits a forced wave provided that the forcing speed c∈(−c2∗,c1∗) 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∈(−c2∗,0)∪(0,c1∗). Then, based on the comparison argument, we prove that the gap formations exist for c>c1∗ and c<−c2∗. Finally, some numeric simulation results are presented to confirm our theoretical results, which also contains the critical cases of c=c1∗ and c=−c2∗.