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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 2 March 2015

Permanent link to this document

Digital Object Identifier


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.

Export citation


  • S. Tang and R. A. Cheke, “Models for integrated pest control and their biological implications,” Mathematical Biosciences, vol. 215, no. 1, pp. 115–125, 2008.
  • S. Tang, Y. Xiao, and R. A. Cheke, “Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak,” Theoretical Population Biology, vol. 73, no. 2, pp. 181–197, 2008.
  • Y. Xiao and F. van den Bosch, “The dynamics of an eco-epidemic model with biological control,” Ecological Modelling, vol. 168, no. 1-2, pp. 203–214, 2003.
  • F. D. Parker, “Management of pest populations by manipulating densities of both hosts and parasites through periodic releases,” in Biological Control, pp. 365–376, Springer, New York, NY, USA, 1971.
  • V. M. Stern, R. F. Smith, R. van den Bosch, and K. S. Hagen, The Integration of Chemical and Biological Control of the Spotted Alfalfa Aphid, University of California, Berkeley, Calif, USA, 1959.
  • J. Liang and S. Tang, “Optimal dosage and economic threshold of multiple pesticide applications for pest control,” Mathematical and Computer Modelling, vol. 51, no. 5-6, pp. 487–503, 2010.
  • J. Liang, S. Tang, R. A. Cheke, and J. Wu, “Adaptive release of natural enemies in a pest-natural enemy system with pesticide resistance,” Bulletin of Mathematical Biology, vol. 75, no. 11, pp. 2167–2195, 2013.
  • S. Tang, J. Liang, Y. Tan, and R. A. Cheke, “Threshold conditions for integrated pest management models with pesticides that have residual effects,” Journal of Mathematical Biology, vol. 66, no. 1-2, pp. 1–35, 2013.
  • S. Tang, J. Liang, Y. Xiao, and R. A. Cheke, “Sliding bifurcations of Filippov two stage pest control models with economic thresholds,” SIAM Journal on Applied Mathematics, vol. 72, no. 4, pp. 1061–1080, 2012.
  • Y. Xiao, X. Xu, and S. Tang, “Sliding mode control of outbreaks of emerging infectious diseases,” Bulletin of Mathematical Biology, vol. 74, no. 10, pp. 2403–2422, 2012.
  • J. Yang, S. Tang, and R. A. Cheke, “Global stability and sliding bifurcations of a non-smooth Gause predator-prey system,” Applied Mathematics and Computation, vol. 224, pp. 9–20, 2013.
  • X. Zhang and S. Tang, “Filippov ratio-dependent prey-predator model with threshold policy control,” Abstract and Applied Analysis, vol. 2013, Article ID 280945, 11 pages, 2013.
  • R. J. H. Beverton and S. J. Holt, The Theory of Fishing, Sea Fisheries, Their Investigation in the United Kingdom, Edward Arnold, London, UK, 1956.
  • S. R.-J. Jang, “Allee effects in a discrete-time host-parasitoid model,” Journal of Difference Equations and Applications, vol. 12, no. 2, pp. 165–181, 2006.
  • S. R. J. Jang and J. L. Yu, “Discrete-time hostcparasitoid models with pest control,” Journal of Biological Dynamics, vol. 6, no. 2, pp. 718–739, 2012.
  • P. Landi, F. Dercole, and S. Rinaldi, “Branching scenarios in eco-evolutionary prey-predator models,” SIAM Journal on Applied Mathematics, vol. 73, no. 4, pp. 1634–1658, 2013.
  • S. Tang, Y. Xiao, N. Wang, and H. Wu, “Piecewise HIV virus dynamic model with CD4$^{+}$ T cell count-guided therapy: I,” Journal of Theoretical Biology, vol. 308, pp. 123–134, 2012.
  • T. Zhao, Y. Xiao, and R. J. Smith, “Non-smooth plant disease models with economic thresholds,” Mathematical Biosciences, vol. 241, no. 1, pp. 34–48, 2013. \endinput