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Global dynamics of a predator–prey system modeling by metaphysiological approach

Author

Listed:
  • Hu, Jiang-Hong
  • Xue, Ya-Kui
  • Sun, Gui-Quan
  • Jin, Zhen
  • Zhang, Juan

Abstract

In this paper, a systematical analysis of a predator–prey system based on metaphysiological approach is proposed, which considers changes in the aggregate biomass density rather than changes in the demographics. Bifurcation behaviors including transcritical and Hopf bifurcation are observed in this type of system, and bubble phenomena can be seized by setting appropriate values for parameters. The obtained results provide some new insights in population dynamics, which play important roles in maintaining population diversity.

Suggested Citation

  • Hu, Jiang-Hong & Xue, Ya-Kui & Sun, Gui-Quan & Jin, Zhen & Zhang, Juan, 2016. "Global dynamics of a predator–prey system modeling by metaphysiological approach," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 369-384.
    • Handle: RePEc:eee:apmaco:v:283:y:2016:i:c:p:369-384
    DOI: 10.1016/j.amc.2016.02.041
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    1. Marten Scheffer & Jordi Bascompte & William A. Brock & Victor Brovkin & Stephen R. Carpenter & Vasilis Dakos & Hermann Held & Egbert H. van Nes & Max Rietkerk & George Sugihara, 2009. "Early-warning signals for critical transitions," Nature, Nature, vol. 461(7260), pages 53-59, September.
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    Cited by:

    1. Lv, Yunfei & Pei, Yongzhen & Wang, Yong, 2019. "Bifurcations and simulations of two predator–prey models with nonlinear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 158-170.
    2. Wen, Haijun & Hou, Shiwang & Liu, Zhaohua & Liu, Yongjiang, 2017. "An optimization algorithm for integrated remanufacturing production planning and scheduling system," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 69-76.
    3. Wang, Caiyun & Qi, Suying, 2018. "Spatial dynamics of a predator-prey system with cross diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 55-60.
    4. Liu, Chanjuan & Zhu, Enqiang, 2017. "Computational ability in games: Individual difference and dynamics," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 313-320.
    5. Bentout, Soufiane & Djilali, Salih & Kumar, Sunil, 2021. "Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    6. Wu, Zeyan & Li, Jianjuan & Liu, Shuying & Zhou, Liuting & Luo, Yang, 2019. "A spatial predator–prey system with non-renewable resources," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 381-391.
    7. Li, Li, 2017. "Transmission dynamics of Ebola virus disease with human mobility in Sierra Leone," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 575-579.
    8. Wu, Zeyan & Li, Jianjuan & Li, Jing & Liu, Shuying & Zhou, Liuting & Luo, Yang, 2017. "Pattern formations of an epidemic model with Allee effect and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 599-606.
    9. Mandal, Gourav & Guin, Lakshmi Narayan & Chakravarty, Santabrata & Rojas-Palma, Alejandro & González-Olivares, Eduardo, 2024. "Allee-induced bubbling phenomena in an interacting species model," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    10. Mortuja, Md Golam & Chaube, Mithilesh Kumar & Kumar, Santosh, 2021. "Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    11. Zhang, Hong-Tao & Li, Li, 2018. "Traveling wave fronts of a single species model with cannibalism and nonlocal effect," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 148-153.

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