Journal of Applied Mathematics

Dynamic Complexity of a Switched Host-Parasitoid Model with Beverton-Holt Growth Concerning Integrated Pest Management

Changcheng Xiang, Zhongyi Xiang, and Yi Yang

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Abstract

The switched discrete host-parasitoid model with Beverton-Holt growth concerning integrated pest management has been proposed, and the switches are guided by the economic threshold (ET). The integrated pest management (IPM) tactics are applied to prevent the economic injury if the density of host population exceeds the ET, and the IPM tactics are called off once the density of host population descends below ET. To begin with, the regular and virtual equilibria of switched system has been discussed by two or three parameter-bifurcation diagrams, which reveal the regions of different types of equilibria. Besides, numerical bifurcation analyses about inherent growth rates show that the switched discrete system may have complicated dynamics behavior including chaos and the coexistence of multiple attractors. Finally, numerical bifurcation analyses about killing rates indicate that the system comply with the Volterra principle, and initial values of both host and parasitoid populations affect the host outbreaks times.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 501423, 10 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305800

Digital Object Identifier
doi:10.1155/2014/501423

Citation

Xiang, Changcheng; Xiang, Zhongyi; Yang, Yi. Dynamic Complexity of a Switched Host-Parasitoid Model with Beverton-Holt Growth Concerning Integrated Pest Management. J. Appl. Math. 2014 (2014), Article ID 501423, 10 pages. doi:10.1155/2014/501423. https://projecteuclid.org/euclid.jam/1425305800


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