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Dynamic complexity of a predator-prey model for ipm with nonlinear impulsive control incorporating a regulatory factor for predator releases
File(s)
TianTangCheke2019MMAppIPM.pdf (8.91 MB)
Published version
Author(s)
Tian, Y
Tang, S
Cheke, RA
Type
Journal Article
Abstract
The suess of integrated pest management depends on spraying the orret amount of pestiides at an appropriate time and releases of natural enemies or pathogens of the pest in appropriate proportions at ritial times, with little ost and minimal effets on the environment. Therefore, ontrol deisions require information on instantaneous killing rates of pestiides and numbers of natural enemies to be released, variables that should depend on the densities of both pest and natural enemy population densities in the field. To desribe suh a ontrol strategy we have proposed a mathematial model of IPM involving releases of natural enemies in relation to a regulatory fator. The threshold ondition for the existene and stability of the pest free periodi solution is provided using a obweb model, the omparison priniple and Floquet theory, whih reveals the effets of nonlinear ontrol ation on pest outbreaks. Bifuration analyses show that the dynamis of the proposed model an be very omplex, inluding multiple attrators and swith-like transition patterns following small random perturbations. Moreover, the random perturbations and nonlinear impulsive ontrol measures ould generate omplex swithing patterns, whih show that the pest population ould have outbreaks in omplex ways due to environmental noise.
Date Issued
2019-01-03
Date Acceptance
2018-12-06
Citation
Mathematical Modelling and Analysis, 2019, 24 (1), pp.134-154
URI
DOI
ISSN
1392-6292
Publisher
Vilnius Gedinimas Technical University
Start Page
134
End Page
154
Journal / Book Title
Mathematical Modelling and Analysis
Volume
24
Issue
1
Copyright Statement
© 2019 The Author(s). Published by VGTU Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Subjects
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
Applied Mathematics
Publication Status
Published