Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response
The dynamic behavior of a predator-prey model with Holling type IV functional response is investigated with respect to impulsive control strategies. The model is analyzed to obtain the conditions under which the system is locally asymptotically stable and permanent. Existence of a positive periodic...
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Format: | Article |
Language: | English |
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Wiley
2012-01-01
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Series: | Discrete Dynamics in Nature and Society |
Online Access: | http://dx.doi.org/10.1155/2012/141272 |
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author | Yanzhen Wang Min Zhao |
author_facet | Yanzhen Wang Min Zhao |
author_sort | Yanzhen Wang |
collection | DOAJ |
description | The dynamic behavior of a predator-prey model with Holling type IV functional response is investigated with respect to impulsive control strategies. The model is analyzed to obtain the conditions under which the system is locally asymptotically stable and permanent. Existence of a positive periodic solution of the system and the boundedness of the system is also confirmed. Furthermore, numerical analysis is used to discover the influence of impulsive perturbations. The system is found to exhibit rich dynamics such as symmetry-breaking pitchfork bifurcation, chaos, and nonunique dynamics. |
format | Article |
id | doaj-art-3f97fb79b49d4cdbbaba5b6e3110430b |
institution | Kabale University |
issn | 1026-0226 1607-887X |
language | English |
publishDate | 2012-01-01 |
publisher | Wiley |
record_format | Article |
series | Discrete Dynamics in Nature and Society |
spelling | doaj-art-3f97fb79b49d4cdbbaba5b6e3110430b2025-02-03T05:47:16ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/141272141272Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional ResponseYanzhen Wang0Min Zhao1School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaSchool of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaThe dynamic behavior of a predator-prey model with Holling type IV functional response is investigated with respect to impulsive control strategies. The model is analyzed to obtain the conditions under which the system is locally asymptotically stable and permanent. Existence of a positive periodic solution of the system and the boundedness of the system is also confirmed. Furthermore, numerical analysis is used to discover the influence of impulsive perturbations. The system is found to exhibit rich dynamics such as symmetry-breaking pitchfork bifurcation, chaos, and nonunique dynamics.http://dx.doi.org/10.1155/2012/141272 |
spellingShingle | Yanzhen Wang Min Zhao Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response Discrete Dynamics in Nature and Society |
title | Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response |
title_full | Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response |
title_fullStr | Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response |
title_full_unstemmed | Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response |
title_short | Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response |
title_sort | dynamic analysis of an impulsively controlled predator prey model with holling type iv functional response |
url | http://dx.doi.org/10.1155/2012/141272 |
work_keys_str_mv | AT yanzhenwang dynamicanalysisofanimpulsivelycontrolledpredatorpreymodelwithhollingtypeivfunctionalresponse AT minzhao dynamicanalysisofanimpulsivelycontrolledpredatorpreymodelwithhollingtypeivfunctionalresponse |