Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion
This paper is concerned with invasion entire solutions of a monostable time periodic Lotka-Volterra competition-diffusion system. We first give the asymptotic behaviors of time periodic traveling wave solutions at infinity by a dynamical approach coupled with the two-sided Laplace transform. Accordi...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017061 |
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| author | Li-Jun Du Wan-Tong Li Jia-Bing Wang |
| author_facet | Li-Jun Du Wan-Tong Li Jia-Bing Wang |
| author_sort | Li-Jun Du |
| collection | DOAJ |
| description | This paper is concerned with invasion entire solutions of a monostable time periodic Lotka-Volterra competition-diffusion system. We first give the asymptotic behaviors of time periodic traveling wave solutions at infinity by a dynamical approach coupled with the two-sided Laplace transform. According to these asymptotic behaviors, we then obtain some key estimates which are crucial for the construction of an appropriate pair of sub-super solutions. Finally, using the sub-super solutions method and comparison principle, we establish the existence of invasion entire solutions which behave as two periodic traveling fronts with different speeds propagating from both sides of x-axis. In other words, we formulate a new invasion way of the superior species to the inferior one in a time periodic environment. |
| format | Article |
| id | doaj-art-87ae35978c864d128fbae3048de07ce3 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-87ae35978c864d128fbae3048de07ce32025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61187121310.3934/mbe.2017061Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusionLi-Jun Du0Wan-Tong Li1Jia-Bing Wang2School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, ChinaThis paper is concerned with invasion entire solutions of a monostable time periodic Lotka-Volterra competition-diffusion system. We first give the asymptotic behaviors of time periodic traveling wave solutions at infinity by a dynamical approach coupled with the two-sided Laplace transform. According to these asymptotic behaviors, we then obtain some key estimates which are crucial for the construction of an appropriate pair of sub-super solutions. Finally, using the sub-super solutions method and comparison principle, we establish the existence of invasion entire solutions which behave as two periodic traveling fronts with different speeds propagating from both sides of x-axis. In other words, we formulate a new invasion way of the superior species to the inferior one in a time periodic environment.https://www.aimspress.com/article/doi/10.3934/mbe.2017061time periodic traveling wavesasymptotic behaviorcomparison principleinvasion entire solution |
| spellingShingle | Li-Jun Du Wan-Tong Li Jia-Bing Wang Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion Mathematical Biosciences and Engineering time periodic traveling waves asymptotic behavior comparison principle invasion entire solution |
| title | Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion |
| title_full | Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion |
| title_fullStr | Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion |
| title_full_unstemmed | Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion |
| title_short | Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion |
| title_sort | invasion entire solutions in a time periodic lotka volterra competition system with diffusion |
| topic | time periodic traveling waves asymptotic behavior comparison principle invasion entire solution |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017061 |
| work_keys_str_mv | AT lijundu invasionentiresolutionsinatimeperiodiclotkavolterracompetitionsystemwithdiffusion AT wantongli invasionentiresolutionsinatimeperiodiclotkavolterracompetitionsystemwithdiffusion AT jiabingwang invasionentiresolutionsinatimeperiodiclotkavolterracompetitionsystemwithdiffusion |