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Dynamic analysis of phytoplankton–zooplankton–fish singular perturbation system on three time-scales

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  • Ai, Xin
  • Zhang, Yue

Abstract

In this paper, a three-time scale plankton–fish singular perturbation system is proposed by considering the Beddington–DeAngelis functional response and intraguild predation (IGP). For (1, 2)-fast–slow systems, the singularity and classification of generic fold points are discussed. The small amplitude oscillations (SAOs) will generate around the weak characteristic direction near the folded node, which provides a theoretical reference for effectively predicting the phenomenon of algal blooms. It is also obtained that the small amplitude oscillation cannot be generated by the singular Hopf bifurcation and the folded node mechanism. For (2, 1)-fast–slow systems, the existence of singular Hopf bifurcation is discussed by using the center manifold reduction method. The stability of the periodic solution of the singular Hopf bifurcation is discussed. Furthermore, the existence and uniqueness of the relaxation oscillation in R3 are researched by using the entry–exit function. In addition, the effect of stochastic factors on the singular perturbation system is considered.

Suggested Citation

  • Ai, Xin & Zhang, Yue, 2025. "Dynamic analysis of phytoplankton–zooplankton–fish singular perturbation system on three time-scales," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:chsofr:v:190:y:2025:i:c:s0960077924012633
    DOI: 10.1016/j.chaos.2024.115711
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    References listed on IDEAS

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    1. Li, Zhenlei & Zhang, Yue, 2024. "Dynamic analysis of a fast slow modified Leslie–Gower predator–prey model with constant harvest and stochastic factor," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 474-499.
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    4. Panja, Prabir & Mondal, Shyamal Kumar & Jana, Dipak Kumar, 2017. "Effects of toxicants on Phytoplankton-Zooplankton-Fish dynamics and harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 389-399.
    5. Ryan F. Heneghan & Jason D. Everett & Julia L. Blanchard & Patrick Sykes & Anthony J. Richardson, 2023. "Climate-driven zooplankton shifts cause large-scale declines in food quality for fish," Nature Climate Change, Nature, vol. 13(5), pages 470-477, May.
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