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Complex dynamics of a discrete-time predator-prey system with Holling IV functional response

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  • Cui, Qianqian
  • Zhang, Qiang
  • Qiu, Zhipeng
  • Hu, Zengyun

Abstract

In this paper, a discrete-time predator-prey system with Holling-IV functional response is studied. We first classify the existence of the fixed points of the system, and further investigate their local stabilities. Then the local bifurcation theory for maps is applied to explore the variety of dynamics of the system. Sufficient conditions for the flip bifurcation and Neimark–Sacker bifurcation are provided. Numerical results demonstrate that the system may have more complex dynamical behaviors including multiple periodic orbits, quasi-periodic orbits and chaotic behavior. The maximum Lyapunov exponent and sensitivity analysis also confirm the chaotic dynamical behaviors of the system.

Suggested Citation

  • Cui, Qianqian & Zhang, Qiang & Qiu, Zhipeng & Hu, Zengyun, 2016. "Complex dynamics of a discrete-time predator-prey system with Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 158-171.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:158-171
    DOI: 10.1016/j.chaos.2016.04.002
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    References listed on IDEAS

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    1. Gao, Shujing & Chen, Lansun, 2005. "The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1013-1023.
    2. 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. Chen, Qiaoling & Teng, Zhidong & Wang, Feng, 2021. "Fold-flip and strong resonance bifurcations of a discrete-time mosquito model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Blé, Gamaliel & Dela-Rosa, Miguel Angel, 2019. "Neimark–Sacker bifurcation in a tritrophic model with defense in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 124-139.
    3. Hu, Zengyun & Teng, Zhidong & Zhang, Tailei & Zhou, Qiming & Chen, Xi, 2017. "Globally asymptotically stable analysis in a discrete time eco-epidemiological system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 20-31.
    4. Banerjee, Ritwick & Das, Pritha & Mukherjee, Debasis, 2018. "Stability and permanence of a discrete-time two-prey one-predator system with Holling Type-III functional response," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 240-248.
    5. Mondal, Chirodeep & Kesh, Dipak & Mukherjee, Debasis, 2023. "Global stability and bifurcation analysis of an infochemical induced three species discrete-time phytoplankton–zooplankton model," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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