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Numerical Analysis of Discrete Switching Prey‐Predator Model for Integrated Pest Management

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  • Changcheng Xiang
  • Yi Yang
  • Zhongyi Xiang
  • Wenjie Qin

Abstract

The switching discrete prey‐predator model concerning integrated pest management has been proposed, and the switches are guided by the economic threshold (ET). To begin with, the regular and virtual equilibria of switching system have been discussed and the key parameter bifurcation diagrams for the existence of equilibria have been proposed, which reveal the three different regions of equilibria. Besides, numerical bifurcation analyses show that the switching discrete system may have complicated dynamics behavior including chaos and the coexistence of multiple attractors. Finally, the effects of key parameters on the switching frequencies and switching times are discussed and the sensitivity analysis of varying parameter values for mean switching times has also been given. The results proved that economic threshold (ET) and the growth rate (α) were the key parameters for pest control.

Suggested Citation

  • Changcheng Xiang & Yi Yang & Zhongyi Xiang & Wenjie Qin, 2016. "Numerical Analysis of Discrete Switching Prey‐Predator Model for Integrated Pest Management," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:8627613
    DOI: 10.1155/2016/8627613
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    References listed on IDEAS

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    1. Changcheng Xiang & Zhongyi Xiang & Yi Yang, 2014. "Dynamic Complexity of a Switched Host-Parasitoid Model with Beverton-Holt Growth Concerning Integrated Pest Management," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-10, May.
    2. Changcheng Xiang & Zhongyi Xiang & Yi Yang, 2014. "Dynamic Complexity of a Switched Host‐Parasitoid Model with Beverton‐Holt Growth Concerning Integrated Pest Management," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
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