Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays
This paper is concerned with a semiratio-dependent predator-prey system with nonmonotonic functional response and two delays. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Change of stability of the positive equilibrium...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/495072 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849467761789501440 |
|---|---|
| author | Ming Zhao |
| author_facet | Ming Zhao |
| author_sort | Ming Zhao |
| collection | DOAJ |
| description | This paper is concerned with a semiratio-dependent predator-prey system with nonmonotonic functional response and two delays. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Change of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a sequence of critical values. The properties of Hopf bifurcation such as direction and stability are determined by using the normal form method and center manifold theorem. Numerical simulations confirm our theoretical findings. |
| format | Article |
| id | doaj-art-e5edfba28ad34a76aa3d867ff6298f1a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e5edfba28ad34a76aa3d867ff6298f1a2025-08-20T03:26:04ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/495072495072Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two DelaysMing Zhao0Software College, Pingdingshan University, Pingdingshan 467000, ChinaThis paper is concerned with a semiratio-dependent predator-prey system with nonmonotonic functional response and two delays. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Change of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a sequence of critical values. The properties of Hopf bifurcation such as direction and stability are determined by using the normal form method and center manifold theorem. Numerical simulations confirm our theoretical findings.http://dx.doi.org/10.1155/2013/495072 |
| spellingShingle | Ming Zhao Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays Abstract and Applied Analysis |
| title | Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays |
| title_full | Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays |
| title_fullStr | Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays |
| title_full_unstemmed | Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays |
| title_short | Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays |
| title_sort | hopf bifurcation analysis for a semiratio dependent predator prey system with two delays |
| url | http://dx.doi.org/10.1155/2013/495072 |
| work_keys_str_mv | AT mingzhao hopfbifurcationanalysisforasemiratiodependentpredatorpreysystemwithtwodelays |