Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays
We consider a predator-prey system with Michaelis-Menten type functional response and two delays. We focus on the case with two unequal and non-zero delays present in the model, study the local stability of the equilibria and the existence of Hopf bifurcation, and then obtain explicit formulas to de...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/835310 |
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| _version_ | 1832557044799897600 |
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| author | Yunxian Dai Yiping Lin Huitao Zhao |
| author_facet | Yunxian Dai Yiping Lin Huitao Zhao |
| author_sort | Yunxian Dai |
| collection | DOAJ |
| description | We consider a predator-prey system with Michaelis-Menten type functional response and two delays. We focus on the case with two unequal and non-zero delays present in the model, study the local stability of the equilibria and the existence of Hopf bifurcation, and then obtain explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation when the delays τ1≠τ2. |
| format | Article |
| id | doaj-art-a7a7a612567a4f82bde733f81b4864d3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a7a7a612567a4f82bde733f81b4864d32025-02-03T05:43:52ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/835310835310Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two DelaysYunxian Dai0Yiping Lin1Huitao Zhao2Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, ChinaDepartment of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, ChinaDepartment of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, ChinaWe consider a predator-prey system with Michaelis-Menten type functional response and two delays. We focus on the case with two unequal and non-zero delays present in the model, study the local stability of the equilibria and the existence of Hopf bifurcation, and then obtain explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation when the delays τ1≠τ2.http://dx.doi.org/10.1155/2014/835310 |
| spellingShingle | Yunxian Dai Yiping Lin Huitao Zhao Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays Abstract and Applied Analysis |
| title | Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays |
| title_full | Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays |
| title_fullStr | Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays |
| title_full_unstemmed | Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays |
| title_short | Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays |
| title_sort | hopf bifurcation and global periodic solutions in a predator prey system with michaelis menten type functional response and two delays |
| url | http://dx.doi.org/10.1155/2014/835310 |
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