Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate
A delayed ecoepidemic model with ratio-dependent transmission rate has been proposed in this paper. Effects of the time delay due to the gestation of the predator are the main focus of our work. Sufficient conditions for local stability and existence of a Hopf bifurcation of the model are derived by...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/5626039 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832554169218629632 |
|---|---|
| author | Wanjun Xia Soumen Kundu Sarit Maitra |
| author_facet | Wanjun Xia Soumen Kundu Sarit Maitra |
| author_sort | Wanjun Xia |
| collection | DOAJ |
| description | A delayed ecoepidemic model with ratio-dependent transmission rate has been proposed in this paper. Effects of the time delay due to the gestation of the predator are the main focus of our work. Sufficient conditions for local stability and existence of a Hopf bifurcation of the model are derived by regarding the time delay as the bifurcation parameter. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out in order to validate our obtained theoretical results. |
| format | Article |
| id | doaj-art-abcf7b1126e14fae965d570560d11d21 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-abcf7b1126e14fae965d570560d11d212025-02-03T05:52:10ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/56260395626039Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission RateWanjun Xia0Soumen Kundu1Sarit Maitra2School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, ChinaNational Institute of Technology Durgapur, Durgapur, West Bengal 713209, IndiaNational Institute of Technology Durgapur, Durgapur, West Bengal 713209, IndiaA delayed ecoepidemic model with ratio-dependent transmission rate has been proposed in this paper. Effects of the time delay due to the gestation of the predator are the main focus of our work. Sufficient conditions for local stability and existence of a Hopf bifurcation of the model are derived by regarding the time delay as the bifurcation parameter. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out in order to validate our obtained theoretical results.http://dx.doi.org/10.1155/2018/5626039 |
| spellingShingle | Wanjun Xia Soumen Kundu Sarit Maitra Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate Journal of Function Spaces |
| title | Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate |
| title_full | Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate |
| title_fullStr | Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate |
| title_full_unstemmed | Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate |
| title_short | Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate |
| title_sort | hopf bifurcation of a delayed ecoepidemic model with ratio dependent transmission rate |
| url | http://dx.doi.org/10.1155/2018/5626039 |
| work_keys_str_mv | AT wanjunxia hopfbifurcationofadelayedecoepidemicmodelwithratiodependenttransmissionrate AT soumenkundu hopfbifurcationofadelayedecoepidemicmodelwithratiodependenttransmissionrate AT saritmaitra hopfbifurcationofadelayedecoepidemicmodelwithratiodependenttransmissionrate |