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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Main Authors: Yanzhen Wang, Min Zhao
Format: Article
Language:English
Published: Wiley 2012-01-01
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
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institution Kabale University
issn 1026-0226
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language English
publishDate 2012-01-01
publisher Wiley
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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