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Dynamic complexity of a host–parasitoid ecological model with the Hassell growth function for the host

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  • Zhu, Lili
  • Zhao, Min

Abstract

This paper investigates a discrete-time host–parasitoid ecological model with Hassell growth function for the host by qualitative analysis and numerical simulation. Local stability analysis of the system is carried out. Many forms of complex dynamics are observed, including chaotic bands with periodic windows, pitchfork and tangent bifurcations, attractor crises, intermittency, supertransients, and non-unique dynamics (meaning that several attractors coexist). The largest Lyapunov exponents are numerically computed to confirm further the complexity of these dynamic behaviors.

Suggested Citation

  • Zhu, Lili & Zhao, Min, 2009. "Dynamic complexity of a host–parasitoid ecological model with the Hassell growth function for the host," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1259-1269.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:3:p:1259-1269
    DOI: 10.1016/j.chaos.2007.10.023
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    References listed on IDEAS

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    1. Xu, Cailin & Boyce, Mark S., 2005. "Dynamic complexities in a mutual interference host–parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 175-182.
    2. Lv, Songjuan & Zhao, Min, 2008. "The dynamic complexity of a three species food chain model," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1469-1480.
    3. Lv, Songjuan & Zhao, Min, 2008. "The dynamic complexity of a host–parasitoid model with a lower bound for the host," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 911-919.
    4. 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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    Cited by:

    1. Zhang, Limin & Zhao, Min, 2009. "Dynamic complexities in a hyperparasitic system with prolonged diapause for host," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1136-1142.
    2. Dai, Chuanjun & Zhao, Min & Chen, Lansun, 2012. "Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 83-97.
    3. Zhang, Limin & Zhang, Chaofeng & Zhao, Min, 2014. "Dynamic complexities in a discrete predator–prey system with lower critical point for the prey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 119-131.

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