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Hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms

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  • Zhao, Hongyong
  • Huang, Xuanxuan
  • Zhang, Xuebing

Abstract

In this paper, we study the dynamics of a bioeconomic plankton model with delay and diffusion terms, in which phytoplankton is assumed to undergo exploitation. Some sufficient conditions ensuring the stability and bifurcation for the model are provided by using stability and bifurcation theory. Our results show that harvest effort can control bifurcation and resume system’s stability in the case of positive economic profit, and over exploitation will result in the extinction of the population which is in line with reality. Finally, some numerical simulations are given to verify the analytical results of nutrient–phytoplankton–zooplankton–fish model.

Suggested Citation

  • Zhao, Hongyong & Huang, Xuanxuan & Zhang, Xuebing, 2015. "Hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 300-315.
    • Handle: RePEc:eee:phsmap:v:421:y:2015:i:c:p:300-315
    DOI: 10.1016/j.physa.2014.11.042
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    References listed on IDEAS

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    1. Upadhyay, Ranjit Kumar & Kumari, Nitu & Rai, Vikas, 2009. "Wave of chaos in a diffusive system: Generating realistic patterns of patchiness in plankton–fish dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 262-276.
    2. Gao, Shujing & Chen, Lansun, 2005. "The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1013-1023.
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    Citations

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    Cited by:

    1. Liu, Chao & Wang, Luping & Zhang, Qingling & Yan, Yun, 2017. "Dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 682-698.
    2. Huang, Chengdai, 2018. "Multiple scales scheme for bifurcation in a delayed extended van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 643-652.
    3. 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.
    4. Gökçe, Aytül & Yazar, Samire & Sekerci, Yadigar, 2020. "Delay induced nonlinear dynamics of oxygen-plankton interactions," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Gökçe, Aytül, 2022. "A dynamic interplay between Allee effect and time delay in a mathematical model with weakening memory," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    6. Liang, Yuqin & Jia, Yunfeng, 2022. "Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    7. Pal, D. & Samanta, G.P. & Mahapatra, G.S., 2017. "Selective harvesting of two competing fish species in the presence of toxicity with time delay," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 74-93.
    8. Liu, Chao & Yu, Longfei & Zhang, Qingling & Li, Yuanke, 2018. "Dynamic analysis of a hybrid bioeconomic plankton system with double time delays and stochastic fluctuations," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 115-137.

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