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Stability and bifurcation of a stage-structured predator–prey model with both discrete and distributed delays

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Listed:
  • Wang, Fengyan
  • Kuang, Yang
  • Ding, Changming
  • Zhang, Shuwen

Abstract

This paper concerns with a new delayed predator–prey model with stage structure on prey, in which the immature prey and the mature prey are preyed by predator and the delay is the length of the immature stage. Mathematical analysis of the model equations is given with regard to invariance of non-negativity, boundedness of solutions, permanence and global stability and nature of equilibria. Our work shows that the stage structure on the prey is one of the important factors that affect the extinction of the predator, and the predation on immature prey is a cause of periodic oscillation of population and can make the behaviors of the system more complex. The predation on the immature and mature prey brings both positive and negative effects on the permanence of the predator, if ignore the predation on immature prey in the system, the stage-structure on prey brings only negative effect on the permanence of the predator.

Suggested Citation

  • Wang, Fengyan & Kuang, Yang & Ding, Changming & Zhang, Shuwen, 2013. "Stability and bifurcation of a stage-structured predator–prey model with both discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 19-27.
    • Handle: RePEc:eee:chsofr:v:46:y:2013:i:c:p:19-27
    DOI: 10.1016/j.chaos.2012.10.003
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    References listed on IDEAS

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    1. Pang, Guoping & Wang, Fengyan & Chen, Lansun, 2009. "Extinction and permanence in delayed stage-structure predator–prey system with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2216-2224.
    2. Wang, Fengyan & Pang, Guoping, 2009. "The global stability of a delayed predator–prey system with two stage-structure," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 778-785.
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    Cited by:

    1. Hoang Pham, 2022. "Mathematical Modeling the Time-Delay Interactions between Tumor Viruses and the Immune System with the Effects of Chemotherapy and Autoimmune Diseases," Mathematics, MDPI, vol. 10(5), pages 1-15, February.
    2. Kundu, Soumen & Maitra, Sarit, 2018. "Dynamics of a delayed predator-prey system with stage structure and cooperation for preys," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 453-460.

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