Dynamic Analysis of a Toxin-Producing Phytoplankton Zooplankton Model with Allee Effect

• Lijuan Chen ^[1] ; Zirui Zhu ^[1] ; Yue Xia ^[1] ; Jitao Sun ^[2] ; Yujuan Chen ^[3]
  1. [1] Fuzhou University

     Fuzhou University

     China

     
  2. [2] Tongji University

     Tongji University

     China

     
  3. [3] Nantong University

     Nantong University

     China

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 3, 2025
• Idioma: inglés
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• Resumen

  • In this paper, two models of toxic phytoplankton and zooplankton with strong or weak Allee effect are investigated. It is discussed whether the equilibria are stable and Hopf bifurcation exists. When the strong Allee effect rate is high and the toxinproducing rate is less, both of two species will remain extinct. However, when the toxin-producing rate increases, the system will possess either a stable limit cycle or a coexistence equilibrium. When the weak Allee effect rate is high, the immediate toxinproducing might result in the occurrence of coexistent equilibrium or a subcritical (supercritical) Hopf bifurcation. A degenerate Hopf bifurcation is also demonstrated by numerical simulation, where the inner limit cycle is stable and the outer one is unstable. For both strong Allee effect and weak Allee effect cases, the obtained results show that immediate production of toxin can aid in the survival of both species and large toxin-producing will be detrimental to the growth of zooplankton. The findings in this research can be viewed as a complement to those with the Allee effect.

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