Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses
We consider the following generalized n-species Lotka-Volterra type and Gilpin-Ayala type competition systems with multiple delays and impulses: xi′(t)=xi(t)[ai(t)-bi(t)xi(t)-∑j=1ncij(t)xjαij(t-ρij(t))-∑j=1ndij(t)xjβij(t-τij(t))-∑j=1neij(t)∫-ηij0kij(s)xjγij(t+s)ds-∑j=1nfij(t)∫-θij0Kij(ξ)xiδij(...
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| Main Authors: | , , , |
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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/10.1155/2013/617824 |
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| author | Zhenguo Luo Liping Luo Jianhua Huang Binxiang Dai |
| author_facet | Zhenguo Luo Liping Luo Jianhua Huang Binxiang Dai |
| author_sort | Zhenguo Luo |
| collection | DOAJ |
| description | We consider the following generalized n-species Lotka-Volterra type and Gilpin-Ayala type competition systems with multiple delays and impulses: xi′(t)=xi(t)[ai(t)-bi(t)xi(t)-∑j=1ncij(t)xjαij(t-ρij(t))-∑j=1ndij(t)xjβij(t-τij(t))-∑j=1neij(t)∫-ηij0kij(s)xjγij(t+s)ds-∑j=1nfij(t)∫-θij0Kij(ξ)xiδij(t+ξ)xjσij(t+ξ)dξ],a.e, t>0, t≠tk; xi(tk+)-xi(tk-)=hikxi(tk), i=1,2,…,n, k∈Z+. By applying the Krasnoselskii fixed-point theorem in a cone of Banach space, we derive some verifiable necessary and sufficient conditions for the existence of positive periodic solutions of the previously mentioned. As applications, some special cases of the previous system are examined and some earlier results are extended and improved. |
| format | Article |
| id | doaj-art-ed96f125a62b43d0a6492890f7497fa6 |
| 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-ed96f125a62b43d0a6492890f7497fa62025-02-03T06:00:45ZengWileyInternational Journal of Differential Equations1687-96431687-96512013-01-01201310.1155/2013/617824617824Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with ImpulsesZhenguo Luo0Liping Luo1Jianhua Huang2Binxiang Dai3Department of Mathematics, Hengyang Normal University, Hengyang 421008, ChinaDepartment of Mathematics, Hengyang Normal University, Hengyang 421008, ChinaDepartment of Mathematics, National University of Defense Technology, Changsha 410073, ChinaSchool of Mathematical Sciences and Statistics, Central South University, Changsha 410075, ChinaWe consider the following generalized n-species Lotka-Volterra type and Gilpin-Ayala type competition systems with multiple delays and impulses: xi′(t)=xi(t)[ai(t)-bi(t)xi(t)-∑j=1ncij(t)xjαij(t-ρij(t))-∑j=1ndij(t)xjβij(t-τij(t))-∑j=1neij(t)∫-ηij0kij(s)xjγij(t+s)ds-∑j=1nfij(t)∫-θij0Kij(ξ)xiδij(t+ξ)xjσij(t+ξ)dξ],a.e, t>0, t≠tk; xi(tk+)-xi(tk-)=hikxi(tk), i=1,2,…,n, k∈Z+. By applying the Krasnoselskii fixed-point theorem in a cone of Banach space, we derive some verifiable necessary and sufficient conditions for the existence of positive periodic solutions of the previously mentioned. As applications, some special cases of the previous system are examined and some earlier results are extended and improved.http://dx.doi.org/10.1155/2013/617824 |
| spellingShingle | Zhenguo Luo Liping Luo Jianhua Huang Binxiang Dai Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses International Journal of Differential Equations |
| title | Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses |
| title_full | Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses |
| title_fullStr | Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses |
| title_full_unstemmed | Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses |
| title_short | Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses |
| title_sort | global positive periodic solutions of generalized n species gilpin ayala delayed competition systems with impulses |
| url | http://dx.doi.org/10.1155/2013/617824 |
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