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Dynamic behavior analysis of phytoplankton–zooplankton system with cell size and time delay

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  • Zhao, Qiuyue
  • Liu, Shutang
  • Tian, Dadong

Abstract

This paper focuses on the dynamic behavior of phytoplankton–zooplankton system with cell size and time delay. Remarkably, the existence of cell size and time delay make the dynamic behavior of the system more close to the real-world situation, essentially different from those in the existing related literature. To analyze the dynamic behavior of the system, the positiveness and boundedness of the solution are first derived. Then, the asymptotic stability of the coexistent equilibrium and Hopf bifurcation are studied by analyzing the associated characteristic equation. Once more, the direction of Hopf bifurcation and the stability of bifurcated periodic solution are determined. Finally, the theoretical results are illustrated by a numerical example.

Suggested Citation

  • Zhao, Qiuyue & Liu, Shutang & Tian, Dadong, 2018. "Dynamic behavior analysis of phytoplankton–zooplankton system with cell size and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 160-168.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:160-168
    DOI: 10.1016/j.chaos.2018.05.014
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    References listed on IDEAS

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    1. Shi, Renxiang & Yu, Jiang, 2017. "Hopf bifurcation analysis of two zooplankton-phytoplankton model with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 62-73.
    2. Zhang, Guodong & Shen, Yi, 2015. "Periodic solutions for a neutral delay Hassell–Varley type predator–prey system," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 443-452.
    3. Zhao, Zhong & Luo, Chengguang & Pang, Liuyong & Chen, Ying, 2016. "Nonlinear modelling of the interaction between phytoplankton and zooplankton with the impulsive feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 255-261.
    4. Wang, Weiming & Zhang, Lei & Wang, Hailing & Li, Zhenqing, 2010. "Pattern formation of a predator–prey system with Ivlev-type functional response," Ecological Modelling, Elsevier, vol. 221(2), pages 131-140.
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    Cited by:

    1. Zhao, Qiuyue & Liu, Shutang & Niu, Xinglong, 2019. "Dynamic behavior analysis of a diffusive plankton model with defensive and offensive effects," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 94-102.
    2. Liu, He & Dai, Chuanjun & Yu, Hengguo & Guo, Qing & Li, Jianbing & Hao, Aimin & Kikuchi, Jun & Zhao, Min, 2023. "Dynamics of a stochastic non-autonomous phytoplankton–zooplankton system involving toxin-producing phytoplankton and impulsive perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 368-386.
    3. Zheng, Yanlin & Gong, Xiang & Gao, Huiwang, 2022. "Selective grazing of zooplankton on phytoplankton defines rapid algal succession and blooms in oceans," Ecological Modelling, Elsevier, vol. 468(C).
    4. Li, Peiluan & Gao, Rong & Xu, Changjin & Li, Ying & Akgül, Ali & Baleanu, Dumitru, 2023. "Dynamics exploration for a fractional-order delayed zooplankton–phytoplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 166(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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