Forced waves and gap formations for a Lotka–Volterra competition model with nonlocal dispersal and shifting habitats - Wang, Jia-Bing; Wu, Chufen (Nonlinear analysis: real world applications, 2021)
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∗.