Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

The bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the sa...

Full description

Bibliographic Details
Main Authors: Xia Liu, Yepeng Xing
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/478315
id doaj-c32e8cd27ee4419ba41b0244ce8576b0
record_format Article
spelling doaj-c32e8cd27ee4419ba41b0244ce8576b02020-11-24T21:24:41ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/478315478315Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant HarvestingXia Liu0Yepeng Xing1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaCollege of Mathematics and Science, Shanghai Normal University, Shanghai 200234, ChinaThe bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the saddle-node bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation, backward bifurcation, separatrix connecting a saddle-node and a saddle bifurcation and heteroclinic bifurcation, and so forth. Our main results reveal much richer dynamics of the system compared to the system with no refuge and harvesting.http://dx.doi.org/10.1155/2013/478315
collection DOAJ
language English
format Article
sources DOAJ
author Xia Liu
Yepeng Xing
spellingShingle Xia Liu
Yepeng Xing
Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting
Abstract and Applied Analysis
author_facet Xia Liu
Yepeng Xing
author_sort Xia Liu
title Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting
title_short Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting
title_full Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting
title_fullStr Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting
title_full_unstemmed Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting
title_sort bifurcations of a ratio-dependent holling-tanner system with refuge and constant harvesting
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description The bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the saddle-node bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation, backward bifurcation, separatrix connecting a saddle-node and a saddle bifurcation and heteroclinic bifurcation, and so forth. Our main results reveal much richer dynamics of the system compared to the system with no refuge and harvesting.
url http://dx.doi.org/10.1155/2013/478315
work_keys_str_mv AT xialiu bifurcationsofaratiodependenthollingtannersystemwithrefugeandconstantharvesting
AT yepengxing bifurcationsofaratiodependenthollingtannersystemwithrefugeandconstantharvesting
_version_ 1725986801028431872

Similar Items