Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay
This paper is concerned with a diffusive predator-prey system with Beddington-DeAngelis functional response and delay effect. By analyzing the distribution of the eigenvalues, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic so...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/463721 |
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| _version_ | 1832553412017782784 |
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| author | Yuzhen Bai Xiaopeng Zhang |
| author_facet | Yuzhen Bai Xiaopeng Zhang |
| author_sort | Yuzhen Bai |
| collection | DOAJ |
| description | This paper is concerned with a diffusive predator-prey system with Beddington-DeAngelis
functional response and delay effect. By analyzing the distribution of the eigenvalues, the stability
of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous
periodic solutions are investigated. Also, it is shown that the small diffusion can affect the Hopf
bifurcations. Finally, the direction and stability of Hopf bifurcations are determined by normal form
theory and center manifold reduction for partial functional differential equations. |
| format | Article |
| id | doaj-art-9876c62366f04accbe3f167dfe857a22 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9876c62366f04accbe3f167dfe857a222025-02-03T05:54:03ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/463721463721Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time DelayYuzhen Bai0Xiaopeng Zhang1School of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaThis paper is concerned with a diffusive predator-prey system with Beddington-DeAngelis functional response and delay effect. By analyzing the distribution of the eigenvalues, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated. Also, it is shown that the small diffusion can affect the Hopf bifurcations. Finally, the direction and stability of Hopf bifurcations are determined by normal form theory and center manifold reduction for partial functional differential equations.http://dx.doi.org/10.1155/2011/463721 |
| spellingShingle | Yuzhen Bai Xiaopeng Zhang Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay Abstract and Applied Analysis |
| title | Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay |
| title_full | Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay |
| title_fullStr | Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay |
| title_full_unstemmed | Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay |
| title_short | Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay |
| title_sort | stability and hopf bifurcation in a diffusive predator prey system with beddington deangelis functional response and time delay |
| url | http://dx.doi.org/10.1155/2011/463721 |
| work_keys_str_mv | AT yuzhenbai stabilityandhopfbifurcationinadiffusivepredatorpreysystemwithbeddingtondeangelisfunctionalresponseandtimedelay AT xiaopengzhang stabilityandhopfbifurcationinadiffusivepredatorpreysystemwithbeddingtondeangelisfunctionalresponseandtimedelay |