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Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays

Author

Listed:
  • Chuanjun Dai
  • Hengguo Yu
  • Qing Guo
  • He Liu
  • Qi Wang
  • Zengling Ma
  • Min Zhao

Abstract

A nutrient-phytoplankton model with multiple delays is studied analytically and numerically. The aim of this paper is to study how the delay factors influence dynamics of interaction between nutrient and phytoplankton. The analytical analysis indicates that the positive equilibrium is always globally asymptotically stable when the delay does not exist. On the contrary, the positive equilibrium loses its stability via Hopf instability induced by delay and then the corresponding periodic solutions emerge. Especially, the stability switches for positive equilibrium occur as the delay is increased. Furthermore, the numerical simulations show that periodic-2 and periodic-3 solutions can appear due to the existence of delays. Numerical results are consistent with the analytical results. Our results demonstrate that the delay has a great impact on the nutrient-phytoplankton dynamics.

Suggested Citation

  • Chuanjun Dai & Hengguo Yu & Qing Guo & He Liu & Qi Wang & Zengling Ma & Min Zhao, 2019. "Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-16, February.
    • Handle: RePEc:hin:complx:3879626
    DOI: 10.1155/2019/3879626
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    References listed on IDEAS

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    Cited by:

    1. Gökçe, Aytül & Yazar, Samire & Sekerci, Yadigar, 2022. "Stability of spatial patterns in a diffusive oxygen–plankton model with time lag effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 109-123.
    2. 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).
    3. Gökçe, Aytül, 2021. "A mathematical study for chaotic dynamics of dissolved oxygen- phytoplankton interactions under environmental driving factors and time lag," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Chen, Zhewen & Zhang, Ruimin & Li, Jiang & Zhang, Shuwen & Wei, Chunjin, 2020. "A stochastic nutrient-phytoplankton model with viral infection and Markov switching," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Tiancai Liao & Hengguo Yu & Chuanjun Dai & Min Zhao, 2019. "Impact of Cell Size Effect on Nutrient-Phytoplankton Dynamics," Complexity, Hindawi, vol. 2019, pages 1-23, November.

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