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Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model

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  • Kejun Zhuang
  • Ying Li
  • Bin Gong
  • Zhichao Jiang

Abstract

In this paper, we study a reaction-diffusion nutrient-phytoplankton model with nutrient recycling delay and toxin-producing phytoplankton. For the delay-free case, we prove that the release rate of toxic chemicals by the toxin-producing phytoplankton can destabilize the system and cause periodic oscillation. For the time-delayed case, we observe that nutrient recycling delay may bring about stability switches and Hopf bifurcation. Moreover, we derive the formula for determining the direction and stability of the bifurcating periodic solutions. Finally, we give some numerical simulations to support the theoretical analyses.

Suggested Citation

  • Kejun Zhuang & Ying Li & Bin Gong & Zhichao Jiang, 2021. "Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model," Complexity, Hindawi, vol. 2021, pages 1-12, October.
    • Handle: RePEc:hin:complx:7943788
    DOI: 10.1155/2021/7943788
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    Cited by:

    1. Guo, Qing & Wang, Yi & Dai, Chuanjun & Wang, Lijun & Liu, He & Li, Jianbing & Tiwari, Pankaj Kumar & Zhao, Min, 2023. "Dynamics of a stochastic nutrient–plankton model with regime switching," Ecological Modelling, Elsevier, vol. 477(C).
    2. Kumari, Sarita & Tiwari, Satish Kumar & Upadhyay, Ranjit Kumar, 2022. "Cross diffusion induced spatiotemporal pattern in diffusive nutrient–plankton model with nutrient recycling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 246-272.

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