The effects of resource limitation on a predator-prey model with control measures as nonlinear pulses
type: Item
instance of: scholarly article
title: The effects of resource limitation on a predator-prey model with control measures as nonlinear pulses
zbMATH Open document ID: 1407.34024
DOI: 10.1155/2014/450935
author: Wenjie Qin
author: Sanyi Tang
author: Robert A. Cheke
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation affects pest population outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coefficients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the significance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide's efficacy against the pest and reduce its effectiveness against the natural enemy, while enhancing the efficiency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Further-more, when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results.
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 7016461
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/450935
OpenAlex ID: W1967177281
Wikidata QID: Q58981787
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description: scientific article; zbMATH DE number 7016461