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Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect

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

Abstract

A delay differential system is investigated based on a previously proposed nutrient-phytoplankton model. The time delay is regarded as a bifurcation parameter. Our aim is to determine how the time delay affects the system. First, we study the existence and local stability of two equilibria using the characteristic equation and identify the condition where a Hopf bifurcation can occur. Second, the formulae that determine the direction of the Hopf bifurcation and the stability of periodic solutions are obtained using the normal form and the center manifold theory. Furthermore, our main results are illustrated using numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:471507
    DOI: 10.1155/2014/471507
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