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Nonlinear Dynamics of a Nutrient‐Plankton Model

Author

Listed:
  • Yapei Wang
  • Min Zhao
  • Chuanjun Dai
  • Xinhong Pan

Abstract

We investigated a nonlinear model of the interaction between nutrients and plankton, which was addressed using a pair of reaction‐advection‐diffusion equations. Based on numerical analysis, we studied a model without diffusion and sinking terms, and we found that the phytoplankton density (a stable state) increased with the increase of nutrient density. We analyzed the model using a linear analysis technique and found that the sinking of phytoplankton could affect the system. If the sinking velocity exceeded a certain critical value, the stable state became unstable and the wavelength of phytoplankton increased with the increase of sinking velocity. Furthermore, band patterns were also produced by our model, which was affected by the diffusion and sinking of phytoplankton. Thus, the change in the diffusion and sinking of phytoplankton led to different spatial distributions of phytoplankton. All of these results are expected to be useful in the study of plankton dynamics in aquatic ecosystems.

Suggested Citation

  • Yapei Wang & Min Zhao & Chuanjun Dai & Xinhong Pan, 2014. "Nonlinear Dynamics of a Nutrient‐Plankton Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:451757
    DOI: 10.1155/2014/451757
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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. Ramin, Maryam & Perhar, Gurbir & Shimoda, Yuko & Arhonditsis, George B., 2012. "Examination of the effects of nutrient regeneration mechanisms on plankton dynamics using aquatic biogeochemical modeling," Ecological Modelling, Elsevier, vol. 240(C), pages 139-155.
    3. Jef Huisman & Nga N. Pham Thi & David M. Karl & Ben Sommeijer, 2006. "Reduced mixing generates oscillations and chaos in the oceanic deep chlorophyll maximum," Nature, Nature, vol. 439(7074), pages 322-325, January.
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    1. Pengfei Wang & Min Zhao & Hengguo Yu & Chuanjun Dai & Nan Wang & Beibei Wang, 2016. "Nonlinear Dynamics of a Toxin‐Phytoplankton‐Zooplankton System with Self‐ and Cross‐Diffusion," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    2. Chuanjun Dai & Min Zhao, 2014. "Nonlinear Analysis in a Nutrient‐Algae‐Zooplankton System with Sinking of Algae," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Mondal, Milton & Rao, Ch. Srinivasa & Zhang, Tonghua, 2026. "Dynamics of a phytoplankton–zooplankton model with three-dimensional patch under the impacts of hydrodynamic conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 665-706.

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