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The effects of resource limitation on a predator-prey model with control measures as nonlinear pulses

The effects of resource limitation on a predator-prey model with control measures as nonlinear pulses

Qin, Wenjie, Tang, Sanyi and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2014) The effects of resource limitation on a predator-prey model with control measures as nonlinear pulses. Mathematical Problems in Engineering, 2014:450935. ISSN 1024-123X (Print), 1563-5147 (Online) (doi:10.1155/2014/450935)

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Abstract

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. Furthermore,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.

Item Type: Article
Additional Information: [1] Copyright © 2014 Wenjie Qin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Uncontrolled Keywords: Holling type II predator-prey model, nonlinear pulse, threshold, complex dynamics, resource limitation, pest-free periodic solution, natural enemies
Subjects: Q Science > QA Mathematics
Q Science > QL Zoology
Faculty / Department / Research Group: Faculty of Engineering & Science > Natural Resources Institute
Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Related URLs:
Last Modified: 07 Jul 2016 11:30
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/11324

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