Distinct Spreading Speeds in a Lotka–Volterra Cooperative System
This paper deals with the spreading speeds in the classical Lotka–Volterra cooperative system, of which the bounds have been studied earlier. By introducing an auxiliary cooperative system and constructing an upper solution, we obtain a sufficient condition to confirm two distinct spreading speeds o...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/4676920 |
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| _version_ | 1832551702842048512 |
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| author | Shuxia Pan |
| author_facet | Shuxia Pan |
| author_sort | Shuxia Pan |
| collection | DOAJ |
| description | This paper deals with the spreading speeds in the classical Lotka–Volterra cooperative system, of which the bounds have been studied earlier. By introducing an auxiliary cooperative system and constructing an upper solution, we obtain a sufficient condition to confirm two distinct spreading speeds of unknown functions. Due to the different average moving speeds of different level sets, we find the existence of propagation terraces in such a cooperative system with constant coefficients. We also present some numerical results to illustrate our results. |
| format | Article |
| id | doaj-art-d30800db520a482d927aff8da496c0ea |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d30800db520a482d927aff8da496c0ea2025-02-03T06:00:49ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/46769204676920Distinct Spreading Speeds in a Lotka–Volterra Cooperative SystemShuxia Pan0School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, ChinaThis paper deals with the spreading speeds in the classical Lotka–Volterra cooperative system, of which the bounds have been studied earlier. By introducing an auxiliary cooperative system and constructing an upper solution, we obtain a sufficient condition to confirm two distinct spreading speeds of unknown functions. Due to the different average moving speeds of different level sets, we find the existence of propagation terraces in such a cooperative system with constant coefficients. We also present some numerical results to illustrate our results.http://dx.doi.org/10.1155/2020/4676920 |
| spellingShingle | Shuxia Pan Distinct Spreading Speeds in a Lotka–Volterra Cooperative System Journal of Mathematics |
| title | Distinct Spreading Speeds in a Lotka–Volterra Cooperative System |
| title_full | Distinct Spreading Speeds in a Lotka–Volterra Cooperative System |
| title_fullStr | Distinct Spreading Speeds in a Lotka–Volterra Cooperative System |
| title_full_unstemmed | Distinct Spreading Speeds in a Lotka–Volterra Cooperative System |
| title_short | Distinct Spreading Speeds in a Lotka–Volterra Cooperative System |
| title_sort | distinct spreading speeds in a lotka volterra cooperative system |
| url | http://dx.doi.org/10.1155/2020/4676920 |
| work_keys_str_mv | AT shuxiapan distinctspreadingspeedsinalotkavolterracooperativesystem |