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Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releases

Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releases

Tian, Yuan, Tang, Sanyi and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2019) Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releases. Mathematical Modelling and Analysis, 24 (1). pp. 134-154. ISSN 1392-6292 (Print), 1648-3510 (Online) (doi:https://doi.org/10.3846/mma.2019.010)

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Abstract

The success of integrated pest management depends on spraying the correct amount of pesticides at an appropriate time and releases of natural enemies or pathogens of the pest in appropriate proportions at critical times, with little cost and minimal effects on the environment. Therefore, control decisions require information on instantaneous killing rates of pesticides 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 describe such a control strategy we have proposed a mathematical model of IPM involving releases of natural enemies in relation to a regulatory factor. The threshold condition for the existence and stability of the pest free periodic solution is provided using a cobweb model, the comparison principle and Floquet theory, which reveals the effects of nonlinear control action on pest outbreaks. Bifurcation analyses show that the dynamics of the proposed model can be very complex, including multiple attractors and switch-like transition patterns following small random perturbations. Moreover, the random perturbations and nonlinear impulsive control measures could generate complex switching patterns, which show that the pest population could have outbreaks in complex ways due to environmental noise.

Item Type: Article
Additional Information: Copyright © 2019 The Author(s). 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.
Uncontrolled Keywords: IPM, nonlinear control action, pest free periodic solution, switch-like transition, random perturbation.
Subjects: S Agriculture > S Agriculture (General)
S Agriculture > SB Plant culture
Faculty / Department / Research Group: Faculty of Engineering & Science
Faculty of Engineering & Science > Natural Resources Institute
Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Faculty of Engineering & Science > Natural Resources Institute > Plant Health Research Group
Last Modified: 24 Jan 2019 15:09
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/22531

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