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Sliding bifurcations of Filippov two stage pest control models with economic thresholds

Sliding bifurcations of Filippov two stage pest control models with economic thresholds

Tang, Sanyi, Liang, Juhua, Xiao, Yanni and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2012) Sliding bifurcations of Filippov two stage pest control models with economic thresholds. SIAM Journal on Applied Mathematics, 72 (4). pp. 1061-1080. ISSN 0036-1399 (Print), 1095-712X (Online) (doi:10.1137/110847020)

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Abstract

In order to control pests, a specific management strategy called the threshold policy is proposed, which can be described by Filippov systems (or piecewise smooth systems). The aim of this work is to investigate a variety of bifurcation phenomena of the equilibria and sliding cycles of Filippov two stage structured population models with density dependent per capita birth rates and
transition rates from the juvenile class into the adult class. It is shown that interadult competition alone can give rise to multiple sliding segments and multiple pseudoequilibria, whilst interadult and interjuvenile competition together can result in rich sliding bifurcations. As the threshold value varies, local sliding bifurcations including boundary node (saddle), tangency, and pseudo–saddlenode bifurcations occur sequentially, and global sliding bifurcations including buckling bifurcations
of the sliding cycles, sliding crossing bifurcations, and pseudohomoclinic bifurcations can be present.Threshold policy control has been shown to be easily implemented and useful in pest management,which can be used to prevent the possibility of multiple pest outbreaks or cause the density of pests to stabilize at a desired level such as an economic threshold.

Item Type: Article
Uncontrolled Keywords: Filippov system, stage structure, sliding bifurcation, sliding homoclinic orbit,economic threshold, pest control
Subjects: S Agriculture > S Agriculture (General)
Faculty / Department / Research Group: Faculty of Engineering & Science > Natural Resources Institute
Faculty of Engineering & Science
Related URLs:
Last Modified: 18 Oct 2016 09:13
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/8776

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