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

By Jia-Bing Wang, Chufen Wu. 2021

71 citations recorded by the source corpus.

Abstract 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 ∈ ( − 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 ∈ ( − c 2 ∗ , 0 ) ∪ ( 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 ∗ .

Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/7098fae0df7d2c9f43dc8a2cd8891103b572a612

Citations in the corpus

• Persistence of species in a predator-prey system with climate change and either nonlocal or local dispersal (2021, unknown): “For a 2-species competition system, we refer to [34] for spatial-temporal dynamics and [32] for the gap formation.”