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Dynamics Analysis of a Nutrient‐Plankton Model with a Time Delay

Author

Listed:
  • Beibei Wang
  • Min Zhao
  • Chuanjun Dai
  • Hengguo Yu
  • Nan Wang
  • Pengfei Wang

Abstract

We analyze a nutrient‐plankton system with a time delay. We choose the time delay as a bifurcation parameter and investigate the stability of a positive equilibrium and the existence of Hopf bifurcations. By using the center manifold theorem and the normal form theory, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are researched. The theoretical results indicate that the time delay can induce a positive equilibrium to switch from a stable to an unstable to a stable state and so on. Numerical simulations show that the theoretical results are correct and feasible, and the system exhibits rich complex dynamics.

Suggested Citation

  • Beibei Wang & Min Zhao & Chuanjun Dai & Hengguo Yu & Nan Wang & Pengfei Wang, 2016. "Dynamics Analysis of a Nutrient‐Plankton Model with a Time Delay," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:9797624
    DOI: 10.1155/2016/9797624
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    References listed on IDEAS

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    1. Xinhong Pan & Min Zhao & Chuanjun Dai & Yapei Wang, 2014. "Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, March.
    2. Roy, Shovonlal, 2009. "The coevolution of two phytoplankton species on a single resource: Allelopathy as a pseudo-mixotrophy," Theoretical Population Biology, Elsevier, vol. 75(1), pages 68-75.
    3. Carlo Bianca & Massimiliano Ferrara & Luca Guerrini, 2013. "The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, December.
    4. Carlo Bianca & Massimiliano Ferrara & Luca Guerrini, 2013. "The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Carlo Bianca & Massimiliano Ferrara & Luca Guerrini, 2013. "Qualitative Analysis of a Retarded Mathematical Framework with Applications to Living Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, November.
    6. Carlo Bianca & Massimiliano Ferrara & Luca Guerrini, 2013. "Qualitative Analysis of a Retarded Mathematical Framework with Applications to Living Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Xinhong Pan & Min Zhao & Chuanjun Dai & Yapei Wang, 2014. "Stability and Hopf Bifurcation Analysis of a Nutrient‐Phytoplankton Model with Delay Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Donald M. Anderson, 1997. "Turning back the harmful red tide," Nature, Nature, vol. 388(6642), pages 513-514, August.
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    Cited by:

    1. Du, Yanfei & Zhang, Cong, 2025. "The effects of delays on stability and spatiotemporal dynamics in a diffusive nutrient-phytoplankton model," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).

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