Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model
We will consider the following nonlinear impulsive delay differential equation N′(t)=r(t)N(t)((K(t)−N(t−mw))/(K(t)+λ(t)N(t−mw))), a.e. t>0, t≠tk, N(tk+)=(1+bk)N(tk), K=1,2,…, where m is a positive integer, r(t), K(t), λ(t) are positive periodic functions of periodic ω. In the nondelay case (m=0),...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/31614 |
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| _version_ | 1832555929154879488 |
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| author | Jian Song |
| author_facet | Jian Song |
| author_sort | Jian Song |
| collection | DOAJ |
| description | We will consider the following nonlinear impulsive delay
differential equation N′(t)=r(t)N(t)((K(t)−N(t−mw))/(K(t)+λ(t)N(t−mw))), a.e. t>0, t≠tk, N(tk+)=(1+bk)N(tk), K=1,2,…, where m is a positive integer, r(t), K(t), λ(t) are positive periodic functions of periodic ω. In the nondelay case (m=0), we show that the above equation has a unique positive periodic solution N*(t) which is globally asymptotically stable. In the delay case, we present sufficient
conditions for the global attractivity of N*(t). Our results imply that under the appropriate periodic impulsive perturbations, the impulsive delay equation preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results. |
| format | Article |
| id | doaj-art-7d5432ffec5a4bb68cec9038fbc3fd4b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-7d5432ffec5a4bb68cec9038fbc3fd4b2025-02-03T05:46:47ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/3161431614Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population modelJian Song0College of Network Education, Lanzhou University of Technology, Lanzhou 730050, Gansu, ChinaWe will consider the following nonlinear impulsive delay differential equation N′(t)=r(t)N(t)((K(t)−N(t−mw))/(K(t)+λ(t)N(t−mw))), a.e. t>0, t≠tk, N(tk+)=(1+bk)N(tk), K=1,2,…, where m is a positive integer, r(t), K(t), λ(t) are positive periodic functions of periodic ω. In the nondelay case (m=0), we show that the above equation has a unique positive periodic solution N*(t) which is globally asymptotically stable. In the delay case, we present sufficient conditions for the global attractivity of N*(t). Our results imply that under the appropriate periodic impulsive perturbations, the impulsive delay equation preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results.http://dx.doi.org/10.1155/DDNS/2006/31614 |
| spellingShingle | Jian Song Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model Discrete Dynamics in Nature and Society |
| title | Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model |
| title_full | Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model |
| title_fullStr | Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model |
| title_full_unstemmed | Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model |
| title_short | Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model |
| title_sort | global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model |
| url | http://dx.doi.org/10.1155/DDNS/2006/31614 |
| work_keys_str_mv | AT jiansong globalattractivityofpositiveperiodicsolutionsforanimpulsivedelayperiodicfoodlimitedpopulationmodel |