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...

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Main Authors: Chongwu Zheng, Fengqin Zhang, Jianquan Li
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
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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.
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institution Kabale University
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language English
publishDate 2014-01-01
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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