Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses
By using a fixed-point theorem of strict-set-contraction, we investigate the existence of positive periodic solutions for a class of the following impulsive neutral Lotka-Volterra system with distributed delays: xi′(t)=xi(t)[ri(t)-∑j=1naij(t)xj(t)-∑j=1nbij(t)∫-τij0fij(ξ)xj(t+ξ)dξ-∑j=1ncij(t)∫-σij...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2013/890281 |
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| _version_ | 1849469483407638528 |
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| author | Zhenguo Luo Liping Luo |
| author_facet | Zhenguo Luo Liping Luo |
| author_sort | Zhenguo Luo |
| collection | DOAJ |
| description | By using a fixed-point theorem of strict-set-contraction, we investigate the existence of positive periodic solutions for a class of the following impulsive neutral Lotka-Volterra system with distributed delays: xi′(t)=xi(t)[ri(t)-∑j=1naij(t)xj(t)-∑j=1nbij(t)∫-τij0fij(ξ)xj(t+ξ)dξ-∑j=1ncij(t)∫-σij0gij(ξ)xj′(t+ξ)dξ], Δxi(tk)=-Iik(xi(tk)), i=1,2,…,n, k=1,2,…. Some verifiable criteria are established easily. |
| format | Article |
| id | doaj-art-fdbd737728cc4fa79035b77af2c219ea |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-fdbd737728cc4fa79035b77af2c219ea2025-08-20T03:25:27ZengWileyInternational Journal of Differential Equations1687-96431687-96512013-01-01201310.1155/2013/890281890281Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and ImpulsesZhenguo Luo0Liping Luo1Department of Mathematics, National University of Defense Technology, Changsha 410073, ChinaDepartment of Mathematics, Hengyang Normal University, Hengyang, Hunan 421008, ChinaBy using a fixed-point theorem of strict-set-contraction, we investigate the existence of positive periodic solutions for a class of the following impulsive neutral Lotka-Volterra system with distributed delays: xi′(t)=xi(t)[ri(t)-∑j=1naij(t)xj(t)-∑j=1nbij(t)∫-τij0fij(ξ)xj(t+ξ)dξ-∑j=1ncij(t)∫-σij0gij(ξ)xj′(t+ξ)dξ], Δxi(tk)=-Iik(xi(tk)), i=1,2,…,n, k=1,2,…. Some verifiable criteria are established easily.http://dx.doi.org/10.1155/2013/890281 |
| spellingShingle | Zhenguo Luo Liping Luo Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses International Journal of Differential Equations |
| title | Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses |
| title_full | Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses |
| title_fullStr | Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses |
| title_full_unstemmed | Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses |
| title_short | Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses |
| title_sort | existence of positive periodic solutions for periodic neutral lotka volterra system with distributed delays and impulses |
| url | http://dx.doi.org/10.1155/2013/890281 |
| work_keys_str_mv | AT zhenguoluo existenceofpositiveperiodicsolutionsforperiodicneutrallotkavolterrasystemwithdistributeddelaysandimpulses AT lipingluo existenceofpositiveperiodicsolutionsforperiodicneutrallotkavolterrasystemwithdistributeddelaysandimpulses |