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The dynamic complexity of a host–parasitoid model with a lower bound for the host

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  • Lv, Songjuan
  • Zhao, Min

Abstract

In this paper, the complex dynamics in a discrete-time model of predator–prey interaction based on a lower bound for the host are presented. Local stability analysis of this model is carried out and many forms of complexities are observed using ecology theories and numerical simulation of the global behavior. Furthermore, the existence of a strange attractor and computation of the largest Lyapunov exponent also demonstrate the chaotic dynamic behavior of the model. The numerical results indicate that computer simulation is a useful method for investigating complex dynamic systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:4:p:911-919
    DOI: 10.1016/j.chaos.2006.07.020
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    References listed on IDEAS

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    1. Castro-e-Silva, Alcides & Bernardes, Américo T., 2001. "Analysis of chaotic behaviour in the population dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 63-70.
    2. 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.
    3. Li, Zhenqing & Wang, Weiming & Wang, Hailing, 2006. "The dynamics of a Beddington-type system with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1229-1239.
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    Cited by:

    1. Xiaorong Ma & Qamar Din & Muhammad Rafaqat & Nasir Javaid & Yongliang Feng, 2020. "A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control," Mathematics, MDPI, vol. 8(4), pages 1-26, April.
    2. Zhao, Min & Wang, Xitao & Yu, Hengguo & Zhu, Jun, 2012. "Dynamics of an ecological model with impulsive control strategy and distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1432-1444.
    3. 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.
    4. Lv, Songjuan & Fang, Zhongmiao, 2009. "The dynamic complexity of a host–parasitoid model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2617-2623.
    5. Zhao, Min & Yu, Hengguo & Zhu, Jun, 2009. "Effects of a population floor on the persistence of chaos in a mutual interference host–parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1245-1250.
    6. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
    7. 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.
    8. Yu, Hengguo & Zhong, Shouming & Ye, Mao, 2009. "Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 619-632.

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