A Holling type II pest and natural enemy model with density dependent IPM strategy
type: Item
instance of: scholarly article
title: A Holling type II pest and natural enemy model with density dependent IPM strategy
zbMATH Open document ID: 1426.92066
DOI: 10.1155/2017/8683207
author: Xia Wang
author: Yuan Tian
author: Sanyi Tang
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: Resource limitations and density dependent releasing of natural enemies during the pest control and integrated pest management will undoubtedly result in nonlinear impulsive control. In order to investigate the effects of those nonlinear control strategies on the successful pest control, we have proposed a pest-natural enemy system concerning integrated pest management with density dependent instant killing rate and releasing rate. In particular, the releasing rate depicts how the number of natural enemy populations released was guided by their current density at the fixed moment. The threshold condition which ensures the existence and global stability of pest-free periodic solution has been discussed first, and the effects of key parameters on the threshold condition reveal that reducing the pulse period does not always benefit pest control; that is, frequent releasing of natural enemies may not be beneficial to the eradication of pests when the density dependent releasing method has been implemented. Moreover, the forward and backward bifurcations could occur once the pest-free periodic solution becomes unstable, and the system could exist with very complex dynamics. All those results confirm that the control actions should be carefully designed once the nonlinear impulsive control measures have been taken for pest management.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 6972602
Wikidata QID: Q59147847
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/8683207
OpenAlex ID: W2625190706
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description: scientific article; zbMATH DE number 6972602