Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvesting
This paper is devoted to studying the existence and nonexistence of traveling wave solution for a nonlocal dispersal delayed predator-prey system with the Beddington-DeAngelis functional response and harvesting. By constructing the suitable upper-lower solutions and applying Schauder's fixed po...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/mbe.2021084?viewType=HTML |
| _version_ | 1818899438186266624 |
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| author | Zhihong Zhao Yan Li Zhaosheng Feng |
| author_facet | Zhihong Zhao Yan Li Zhaosheng Feng |
| author_sort | Zhihong Zhao |
| collection | DOAJ |
| description | This paper is devoted to studying the existence and nonexistence of traveling wave solution for a nonlocal dispersal delayed predator-prey system with the Beddington-DeAngelis functional response and harvesting. By constructing the suitable upper-lower solutions and applying Schauder's fixed point theorem, we show that there exists a positive constant $ c^* $ such that the system possesses a traveling wave solution for any given $ c > c^* $. Moreover, the asymptotic behavior of traveling wave solution at infinity is obtained by the contracting rectangles method. The existence of traveling wave solution for $ c = c^* $ is established by means of Corduneanu's theorem. The nonexistence of traveling wave solution in the case of $ c < c^* $ is also discussed. |
| first_indexed | 2024-12-19T19:47:58Z |
| format | Article |
| id | doaj.art-6a95d126785f4bf0a57b6d15cf76c022 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-19T19:47:58Z |
| publishDate | 2021-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-6a95d126785f4bf0a57b6d15cf76c0222022-12-21T20:08:05ZengAIMS PressMathematical Biosciences and Engineering1551-00182021-04-011821629165210.3934/mbe.2021084Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvestingZhihong Zhao0Yan Li 1Zhaosheng Feng21. School of Mathematics and Physics, University of Science & Technology Beijing, Beijing 100083, China1. School of Mathematics and Physics, University of Science & Technology Beijing, Beijing 100083, China2. School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USAThis paper is devoted to studying the existence and nonexistence of traveling wave solution for a nonlocal dispersal delayed predator-prey system with the Beddington-DeAngelis functional response and harvesting. By constructing the suitable upper-lower solutions and applying Schauder's fixed point theorem, we show that there exists a positive constant $ c^* $ such that the system possesses a traveling wave solution for any given $ c > c^* $. Moreover, the asymptotic behavior of traveling wave solution at infinity is obtained by the contracting rectangles method. The existence of traveling wave solution for $ c = c^* $ is established by means of Corduneanu's theorem. The nonexistence of traveling wave solution in the case of $ c < c^* $ is also discussed.http://www.aimspress.com/article/doi/10.3934/mbe.2021084?viewType=HTMLpredator-prey modelbeddington-deangelis functional responsetraveling wave solutionnonlocal dispersal equationupper-lower solutionsasymptotic behavior |
| spellingShingle | Zhihong Zhao Yan Li Zhaosheng Feng Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvesting Mathematical Biosciences and Engineering predator-prey model beddington-deangelis functional response traveling wave solution nonlocal dispersal equation upper-lower solutions asymptotic behavior |
| title | Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvesting |
| title_full | Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvesting |
| title_fullStr | Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvesting |
| title_full_unstemmed | Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvesting |
| title_short | Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvesting |
| title_sort | traveling wave phenomena in a nonlocal dispersal predator prey system with the beddington deangelis functional response and harvesting |
| topic | predator-prey model beddington-deangelis functional response traveling wave solution nonlocal dispersal equation upper-lower solutions asymptotic behavior |
| url | http://www.aimspress.com/article/doi/10.3934/mbe.2021084?viewType=HTML |
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