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 c1∗ and c2∗ such that the system admits a forced wave provided that the forcing speed c∈(−...
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| Published in | Nonlinear analysis: real world applications Vol. 58; p. 103208 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.04.2021
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| 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 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∗. |
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| AbstractList | 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∗. |
| ArticleNumber | 103208 |
| Author | Wu, Chufen Wang, Jia-Bing |
| Author_xml | – sequence: 1 givenname: Jia-Bing orcidid: 0000-0001-9270-7668 surname: Wang fullname: Wang, Jia-Bing email: wangjb@cug.edu.cn organization: School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, People’s Republic of China – sequence: 2 givenname: Chufen surname: Wu fullname: Wu, Chufen email: wucfmath@fosu.edu.cn organization: School of Mathematics and Big Data, Foshan University, Foshan 528000, People’s Republic of China |
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| Keywords | Forced waves Shifting habitats Lotka–Volterra competition model Gap formations Nonlocal dispersal |
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