Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

A ratio-dependent predator-prey system with Holling type III functional response and feedback controls is proposed. By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the s...

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Main Author: Jinghui Yang
Format: Article
Language:English
Published: Hindawi Limited 2008-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2008/186539
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spelling doaj-ce33d4a7e078411aa421f54b5e9956902020-11-25T01:05:12ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/186539186539Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback ControlsJinghui Yang0College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, ChinaA ratio-dependent predator-prey system with Holling type III functional response and feedback controls is proposed. By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the system are obtained. After that, under some suitable conditions, we show that the predator species y will be driven to extinction. Examples together with their numerical simulations show that the main results are verifiable.http://dx.doi.org/10.1155/2008/186539
collection DOAJ
language English
format Article
sources DOAJ
author Jinghui Yang
spellingShingle Jinghui Yang
Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls
Discrete Dynamics in Nature and Society
author_facet Jinghui Yang
author_sort Jinghui Yang
title Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls
title_short Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls
title_full Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls
title_fullStr Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls
title_full_unstemmed Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls
title_sort dynamics behaviors of a discrete ratio-dependent predator-prey system with holling type iii functional response and feedback controls
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2008-01-01
description A ratio-dependent predator-prey system with Holling type III functional response and feedback controls is proposed. By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the system are obtained. After that, under some suitable conditions, we show that the predator species y will be driven to extinction. Examples together with their numerical simulations show that the main results are verifiable.
url http://dx.doi.org/10.1155/2008/186539
work_keys_str_mv AT jinghuiyang dynamicsbehaviorsofadiscreteratiodependentpredatorpreysystemwithhollingtypeiiifunctionalresponseandfeedbackcontrols
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