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Complex dynamics and bifurcation analysis of host–parasitoid models with impulsive control strategy

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  • Yang, Jin
  • Tang, Sanyi
  • Tan, Yuanshun

Abstract

In this paper, we propose and analyse two type host–parasitoid models with integrated pest management (IPM) interventions as impulsive control strategies. For fixed pulsed model, the threshold condition for the global stability of the host-eradication periodic solution is provided, and the effects of key parameters including the impulsive period, proportionate killing rate, instantaneous search rate, releasing constant, survival rate and the proportionate release rate on the threshold condition are discussed. Then latin hypercube sampling /partial rank correlation coefficients are used to carry out sensitivity analyses to determine the significance of each parameters. Further, bifurcation analyses are presented and the results show that coexistence of attractors existed for a wide range of parameters, and the switch-like transitions among these attractors indicate that varying dosages and frequencies of insecticide applications and numbers of parasitoid released are crucial for IPM strategy. For unfixed pulsed model, the results show that this model exists very complex dynamics and the host population can be controlled below ET, and it implies that the modelling methods are helpful for improving optimal strategies to design appropriate IPM.

Suggested Citation

  • Yang, Jin & Tang, Sanyi & Tan, Yuanshun, 2016. "Complex dynamics and bifurcation analysis of host–parasitoid models with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 522-532.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:522-532
    DOI: 10.1016/j.chaos.2016.07.006
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    References listed on IDEAS

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    1. Jin Yang & Min Zhao, 2011. "Complex Behavior in a Fish Algae Consumption Model with Impulsive Control Strategy," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-17, December.
    2. Tang, Sanyi & Xiao, Yanni & Cheke, Robert A., 2008. "Multiple attractors of host–parasitoid models with integrated pest management strategies: Eradication, persistence and outbreak," Theoretical Population Biology, Elsevier, vol. 73(2), pages 181-197.
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    Cited by:

    1. Liu, Jingna & Qi, Qi & Liu, Bing & Gao, Shujing, 2023. "Pest control switching models with instantaneous and non-instantaneous impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 926-938.

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