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Asymptotic behavior of a hierarchical size-structured Phytoplankton–Zooplankton model with distributed delay

Author

Listed:
  • Chen, Fangru
  • Han, Huili
  • Hu, Jing

Abstract

Plankton plays a pivotal role in maintaining the stability of marine food webs and regulating the carbon cycle. Due to its sensitivity to water temperature and competitive interactions, this study develops a hierarchical size-structured phytoplankton–zooplankton model with distributed delay. To establish the well-posedness of the system, we first linearize the nonlinear system around its positive stationary solution and formulate it as an abstract Cauchy problem. Next, within the framework of C0-semigroup theory, we employ spectral analysis and the characteristic equation method to investigate the local asymptotic stability and instability conditions of the positive stationary solution, as well as to explore the phenomenon of asynchronous exponential growth in the system. In particular, by introducing a threshold function F(P,Q), we derive stability criteria for the zooplankton-free stationary solution. Finally, numerical simulations are performed to validate the model’s effectiveness in predicting population dynamics and environmental responses under varying conditions.

Suggested Citation

  • Chen, Fangru & Han, Huili & Hu, Jing, 2026. "Asymptotic behavior of a hierarchical size-structured Phytoplankton–Zooplankton model with distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:chsofr:v:204:y:2026:i:c:s0960077925017801
    DOI: 10.1016/j.chaos.2025.117766
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    References listed on IDEAS

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