Dynamics behaviors of a discrete ratio-dependent predator-prey system with Holling type III functional response and feedback controls
type: Item
instance of: scholarly article
title: Dynamics behaviors of a discrete ratio-dependent predator-prey system with Holling type III functional response and feedback controls
zbMATH Open document ID: 1161.39020
DOI: 10.1155/2008/186539
author: Jinghui Yang
published in: Discrete Dynamics in Nature and Society
publication date: 2009-04-01T00:00:00Z
full work available at URL: https://eudml.org/doc/129900
review text: Summary: 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.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 93B52
zbMATH DE Number: 5538682
zbMATH Keywords: ratio-dependent predator-prey system
zbMATH Keywords: Holling type III functional response
zbMATH Keywords: feedback controls
zbMATH Keywords: Lyapunov function
zbMATH Keywords: difference equation
zbMATH Keywords: permanence
zbMATH Keywords: global attractivity
MaRDI profile type: Publication
Wikidata QID: Q58644443
OpenAlex ID: W1963967810
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description: scientific article; zbMATH DE number 5538682