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Dynamic analysis of a kind of species control model concerning impulsively releasing pathogen and infective predator

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  • Guo, Hongjian
  • Chen, Lansun
  • Song, Xinyu

Abstract

A kind of species control model concerning impulsive releasing pathogen and infective predator is presented. By using the Floquet theory and comparison theorem of impulsive differential equation, the extinction and permanence of system are discussed and the corresponding conditions are obtained, respectively. Finally, the practical meanings of those conditions are explained and the theoretical results are confirmed by numerical simulations. Besides, with the period of impulsive release varying, the numerical simulations also show that the system displays a series of complex phenomena which include period-doubling cascade, chaos and periodic window, etc.

Suggested Citation

  • Guo, Hongjian & Chen, Lansun & Song, Xinyu, 2009. "Dynamic analysis of a kind of species control model concerning impulsively releasing pathogen and infective predator," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1326-1336.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1326-1336
    DOI: 10.1016/j.chaos.2009.03.021
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    References listed on IDEAS

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    1. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaos in periodically forced Holling type IV predator–prey system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 980-990.
    2. Guo, Hongjian & Song, Xinyu, 2008. "An impulsive predator–prey system with modified Leslie–Gower and Holling type II schemes," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1320-1331.
    3. Zhang, Yujuan & Xiu, Zhilong & Chen, Lansun, 2005. "Dynamic complexity of a two-prey one-predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 131-139.
    4. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaos in periodically forced Holling type II predator–prey system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 367-376.
    5. Song, Xinyu & Li, Yongfeng, 2007. "Dynamic complexities of a Holling II two-prey one-predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 463-478.
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