Permanence for two-species Lotka-Volterra systems with delays
The permanence of the following Lotka-Volterra system with time delays$\dot{x}_ 1(t) = x_1(t)[r_1 - a_1x_1(t) + a_11x_1(t - \tau_11) + a_12x_2(t - \tau_12)]$,$\dot{x}_ 2(t) = x_2(t)[r_2 - a_2x_2(t) + a_21x_1(t - \tau_21) + a_22x_2(t - \tau_22)]$,is considered. With intraspecific competition, it is p...
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AIMS Press
2005-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.137 |
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| author | Suqing Lin Zhengyi Lu |
| author_facet | Suqing Lin Zhengyi Lu |
| author_sort | Suqing Lin |
| collection | DOAJ |
| description | The permanence of the following Lotka-Volterra system with time delays$\dot{x}_ 1(t) = x_1(t)[r_1 - a_1x_1(t) + a_11x_1(t - \tau_11) + a_12x_2(t - \tau_12)]$,$\dot{x}_ 2(t) = x_2(t)[r_2 - a_2x_2(t) + a_21x_1(t - \tau_21) + a_22x_2(t - \tau_22)]$,is considered. With intraspecific competition, it is proved that in competitive case, the system is permanent if and only if the interaction matrix of the system satisfies condition (C1) and in cooperative case it is proved that condition (C2) is sufficient for the permanence of the system. |
| format | Article |
| id | doaj-art-2e1bb1e68e2f43d5a0efed5686daad07 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-2e1bb1e68e2f43d5a0efed5686daad072025-01-24T01:51:11ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-10-013113714410.3934/mbe.2006.3.137Permanence for two-species Lotka-Volterra systems with delaysSuqing Lin0Zhengyi Lu1Department of Mathematics, Sichuan Normal University, Chengdu 610068Department of Mathematics, Wenzhou University, Wenzhou, 325035The permanence of the following Lotka-Volterra system with time delays$\dot{x}_ 1(t) = x_1(t)[r_1 - a_1x_1(t) + a_11x_1(t - \tau_11) + a_12x_2(t - \tau_12)]$,$\dot{x}_ 2(t) = x_2(t)[r_2 - a_2x_2(t) + a_21x_1(t - \tau_21) + a_22x_2(t - \tau_22)]$,is considered. With intraspecific competition, it is proved that in competitive case, the system is permanent if and only if the interaction matrix of the system satisfies condition (C1) and in cooperative case it is proved that condition (C2) is sufficient for the permanence of the system.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.137permanence.lotka-volterra systemdelays |
| spellingShingle | Suqing Lin Zhengyi Lu Permanence for two-species Lotka-Volterra systems with delays Mathematical Biosciences and Engineering permanence. lotka-volterra system delays |
| title | Permanence for two-species Lotka-Volterra systems with delays |
| title_full | Permanence for two-species Lotka-Volterra systems with delays |
| title_fullStr | Permanence for two-species Lotka-Volterra systems with delays |
| title_full_unstemmed | Permanence for two-species Lotka-Volterra systems with delays |
| title_short | Permanence for two-species Lotka-Volterra systems with delays |
| title_sort | permanence for two species lotka volterra systems with delays |
| topic | permanence. lotka-volterra system delays |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.137 |
| work_keys_str_mv | AT suqinglin permanencefortwospecieslotkavolterrasystemswithdelays AT zhengyilu permanencefortwospecieslotkavolterrasystemswithdelays |