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Hopf‐Pitchfork Bifurcation in a Phytoplankton‐Zooplankton Model with Delays

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  • Jia-Fang Zhang
  • Dan Zhang

Abstract

The purpose of this paper is to study the dynamics of a phytoplankton‐zooplankton model with toxin delay. By studying the distribution of the eigenvalues of the associated characteristic equation, the pitchfork bifurcation curve of the system is obtained. Furthermore, on the pitchfork bifurcation curve, we find that the system can undergo a Hopf bifurcation at the positive equilibrium, and we derive the critical values where Hopf‐Pitchfork bifurcation occurs.

Suggested Citation

  • Jia-Fang Zhang & Dan Zhang, 2013. "Hopf‐Pitchfork Bifurcation in a Phytoplankton‐Zooplankton Model with Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:340174
    DOI: 10.1155/2013/340174
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    References listed on IDEAS

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    1. Chakraborty, Subhendu & Roy, Shovonlal & Chattopadhyay, J., 2008. "Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: A mathematical model," Ecological Modelling, Elsevier, vol. 213(2), pages 191-201.
    2. Das, Kalyan & Ray, Santanu, 2008. "Effect of delay on nutrient cycling in phytoplankton–zooplankton interactions in estuarine system," Ecological Modelling, Elsevier, vol. 215(1), pages 69-76.
    3. 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.
    4. Swati Khare & O. P. Misra & Chhatrapal Singh & Joydip Dhar, 2011. "Role of Delay on Planktonic Ecosystem in the Presence of a Toxic Producing Phytoplankton," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-16, October.
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