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<p>In this paper, we introduce and examine a diffusive zooplankton–phytoplankton model that incorporates the effects of toxins and memory-based diffusion, characterized by a delayed phytoplankton-taxis term. We first establish the existence and uniform boundedness of solutions. Following this, we analyze the stability of positive constant equilibria, discovering that memory delay can trigger Hopf bifurcation, leading to the emergence of spatially inhomogeneous periodic solutions. This finding suggests that memory-based diffusion facilitates pattern formation, contrasting with the outcomes of models that include only phytoplankton-taxis. Numerical simulations demonstrate that varying toxin input rates can lead to the extinction of phytoplankton and zooplankton, and that increasing the delay may also cause population collapse.</p>

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Dynamics of a memory-based diffusion zooplankton–phytoplankton model with effect of toxins

  • 期刊论文

  • 发表日期：

    2025年2月21日

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  • Yutong Shao,
  • Xuebing Zhang,
  • Shunji Li

摘要

In this paper, we introduce and examine a diffusive zooplankton–phytoplankton model that incorporates the effects of toxins and memory-based diffusion, characterized by a delayed phytoplankton-taxis term. We first establish the existence and uniform boundedness of solutions. Following this, we analyze the stability of positive constant equilibria, discovering that memory delay can trigger Hopf bifurcation, leading to the emergence of spatially inhomogeneous periodic solutions. This finding suggests that memory-based diffusion facilitates pattern formation, contrasting with the outcomes of models that include only phytoplankton-taxis. Numerical simulations demonstrate that varying toxin input rates can lead to the extinction of phytoplankton and zooplankton, and that increasing the delay may also cause population collapse.