Bifurcation analysis for a delayed food chain system with two functional responses
A delayed three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is investigated. By analyzing the distribution of the roots of the associated characteristic equation, we get the sufficient conditions for the stability of the positive equil...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2013-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2357 |
| _version_ | 1797830682609713152 |
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| author | Zizhen Zhang Huizhong Yang Juan Liu |
| author_facet | Zizhen Zhang Huizhong Yang Juan Liu |
| author_sort | Zizhen Zhang |
| collection | DOAJ |
| description | A delayed three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is investigated. By analyzing the distribution of the roots of the associated characteristic equation, we get the sufficient conditions for the stability of the positive equilibrium and the existence of Hopf bifurcation. In particular, using the normal form theory and center manifold theorem, the properties of Hopf bifurcation such as direction and stability are determined. Finally, numerical simulations are given to substantiate the theoretical results. |
| first_indexed | 2024-04-09T13:39:59Z |
| format | Article |
| id | doaj.art-ef82e7700bd84e23a6361aaa4e0c6c19 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:59Z |
| publishDate | 2013-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-ef82e7700bd84e23a6361aaa4e0c6c192023-05-09T07:53:03ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752013-09-0120135311310.14232/ejqtde.2013.1.532357Bifurcation analysis for a delayed food chain system with two functional responsesZizhen Zhang0Huizhong Yang1Juan Liu2Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, PR China Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University,,No 1800 Lihu Avenue, Wuxi, Jiangsu, 214122, P. R.CDepartment of Mathematics and Physics, Bengbu College, Bengbu,233030, ChinaA delayed three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is investigated. By analyzing the distribution of the roots of the associated characteristic equation, we get the sufficient conditions for the stability of the positive equilibrium and the existence of Hopf bifurcation. In particular, using the normal form theory and center manifold theorem, the properties of Hopf bifurcation such as direction and stability are determined. Finally, numerical simulations are given to substantiate the theoretical results.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2357bifurcationdelayfood chain systemstabilityperiodic solution |
| spellingShingle | Zizhen Zhang Huizhong Yang Juan Liu Bifurcation analysis for a delayed food chain system with two functional responses Electronic Journal of Qualitative Theory of Differential Equations bifurcation delay food chain system stability periodic solution |
| title | Bifurcation analysis for a delayed food chain system with two functional responses |
| title_full | Bifurcation analysis for a delayed food chain system with two functional responses |
| title_fullStr | Bifurcation analysis for a delayed food chain system with two functional responses |
| title_full_unstemmed | Bifurcation analysis for a delayed food chain system with two functional responses |
| title_short | Bifurcation analysis for a delayed food chain system with two functional responses |
| title_sort | bifurcation analysis for a delayed food chain system with two functional responses |
| topic | bifurcation delay food chain system stability periodic solution |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2357 |
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