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Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism

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  • Haiyun Bai
  • Yanhui Zhai

Abstract

We research the dynamics of the chemostat model with time delay. The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. By using the normal form theory and center manifold method, we derive the explicit formulas determining the stability and direction of bifurcating periodic solutions. Finally, some numerical simulations are given to illustrate the effectiveness of our results.

Suggested Citation

  • Haiyun Bai & Yanhui Zhai, 2013. "Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, April.
    • Handle: RePEc:hin:jnlaaa:829045
    DOI: 10.1155/2013/829045
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