一类时滞捕食系统的Hopf分支(Hopf bifurcation analysis of a predator-prey system with delays)
A delayed predator-prey system with modified Leslie-Gower and Holling type IV schemes are analyzed. The local asymptotic stability and the existence of the periodic solutions via Hopf bifurcation with respect to the two delays are investigated. By analyzing the associated characteristic equation, su...
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2013-11-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2013.06.002 |
| _version_ | 1827303028017856512 |
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| author | LIUJuan(刘娟) LIYi-min(李医民) |
| author_facet | LIUJuan(刘娟) LIYi-min(李医民) |
| author_sort | LIUJuan(刘娟) |
| collection | DOAJ |
| description | A delayed predator-prey system with modified Leslie-Gower and Holling type IV schemes are analyzed. The local asymptotic stability and the existence of the periodic solutions via Hopf bifurcation with respect to the two delays are investigated. By analyzing the associated characteristic equation, sufficient conditions for local asymptotic stability of the positive equilibrium and the Hopf bifurcation occurring for the possible combination of the two delays are obtained. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are also presented for the support of our analytical findings. |
| first_indexed | 2024-04-24T16:54:57Z |
| format | Article |
| id | doaj.art-19dc00345e654257b6e847f782af6cd2 |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T16:54:57Z |
| publishDate | 2013-11-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-19dc00345e654257b6e847f782af6cd22024-03-29T01:58:32ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972013-11-0140661862610.3785/j.issn.1008-9497.2013.06.002一类时滞捕食系统的Hopf分支(Hopf bifurcation analysis of a predator-prey system with delays)LIUJuan(刘娟)0LIYi-min(李医民)1( 1. Department of Mathematics and Physics, Bengbu College, Bengbu 233030, Anhui Province, China)( 2. Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu Province, China)A delayed predator-prey system with modified Leslie-Gower and Holling type IV schemes are analyzed. The local asymptotic stability and the existence of the periodic solutions via Hopf bifurcation with respect to the two delays are investigated. By analyzing the associated characteristic equation, sufficient conditions for local asymptotic stability of the positive equilibrium and the Hopf bifurcation occurring for the possible combination of the two delays are obtained. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are also presented for the support of our analytical findings.https://doi.org/10.3785/j.issn.1008-9497.2013.06.002hopf bifurcationdelayspredator-prey systemperiodic solution |
| spellingShingle | LIUJuan(刘娟) LIYi-min(李医民) 一类时滞捕食系统的Hopf分支(Hopf bifurcation analysis of a predator-prey system with delays) Zhejiang Daxue xuebao. Lixue ban hopf bifurcation delays predator-prey system periodic solution |
| title | 一类时滞捕食系统的Hopf分支(Hopf bifurcation analysis of a predator-prey system with delays) |
| title_full | 一类时滞捕食系统的Hopf分支(Hopf bifurcation analysis of a predator-prey system with delays) |
| title_fullStr | 一类时滞捕食系统的Hopf分支(Hopf bifurcation analysis of a predator-prey system with delays) |
| title_full_unstemmed | 一类时滞捕食系统的Hopf分支(Hopf bifurcation analysis of a predator-prey system with delays) |
| title_short | 一类时滞捕食系统的Hopf分支(Hopf bifurcation analysis of a predator-prey system with delays) |
| title_sort | 一类时滞捕食系统的hopf分支 hopf bifurcation analysis of a predator prey system with delays |
| topic | hopf bifurcation delays predator-prey system periodic solution |
| url | https://doi.org/10.3785/j.issn.1008-9497.2013.06.002 |
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