Canard Limit Cycle of the Holling-Tanner Model
By using the singular perturbation theory on canard cycles, we investigate the canard phenomenon for the Holling-Tanner model with the intrinsic growth rate of the predator small enough. The obtained result shows that there may be at most one canard limit cycle, and the range of small parameters is...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/856475 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849402412126699520 |
|---|---|
| author | Chongwu Zheng Fengqin Zhang Jianquan Li |
| author_facet | Chongwu Zheng Fengqin Zhang Jianquan Li |
| author_sort | Chongwu Zheng |
| collection | DOAJ |
| description | By using the singular perturbation theory on canard cycles, we investigate the canard phenomenon for the Holling-Tanner model with the intrinsic
growth rate of the predator small enough. The obtained result shows that there may be at most one canard limit cycle, and the range of small parameters is estimated. The phenomenon of outbreak is explained. |
| format | Article |
| id | doaj-art-8310c9f1f0024efda0a2a3147ec3e04a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8310c9f1f0024efda0a2a3147ec3e04a2025-08-20T03:37:32ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/856475856475Canard Limit Cycle of the Holling-Tanner ModelChongwu Zheng0Fengqin Zhang1Jianquan Li2Department of Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, ChinaDepartment of Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, ChinaScience College, Air Force Engineering University, Xi’an 710051, ChinaBy using the singular perturbation theory on canard cycles, we investigate the canard phenomenon for the Holling-Tanner model with the intrinsic growth rate of the predator small enough. The obtained result shows that there may be at most one canard limit cycle, and the range of small parameters is estimated. The phenomenon of outbreak is explained.http://dx.doi.org/10.1155/2014/856475 |
| spellingShingle | Chongwu Zheng Fengqin Zhang Jianquan Li Canard Limit Cycle of the Holling-Tanner Model Discrete Dynamics in Nature and Society |
| title | Canard Limit Cycle of the Holling-Tanner Model |
| title_full | Canard Limit Cycle of the Holling-Tanner Model |
| title_fullStr | Canard Limit Cycle of the Holling-Tanner Model |
| title_full_unstemmed | Canard Limit Cycle of the Holling-Tanner Model |
| title_short | Canard Limit Cycle of the Holling-Tanner Model |
| title_sort | canard limit cycle of the holling tanner model |
| url | http://dx.doi.org/10.1155/2014/856475 |
| work_keys_str_mv | AT chongwuzheng canardlimitcycleofthehollingtannermodel AT fengqinzhang canardlimitcycleofthehollingtannermodel AT jianquanli canardlimitcycleofthehollingtannermodel |