Multiple limit cycles in the chemostat with variable yield

  • Pilyugin S
  • Waltman P
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Abstract

The global asymptotic behavior of solutions of the variable yield model is determined. The model generalizes the classical Monod model and it assumes that the yield is an increasing function of the nutrient concentration. In contrast to the Monod model, it is demonstrated that the variable yield model exhibits sustained oscillations. Moreover, it is shown that the variable yield model may undergo a subcritical Hopf bifurcation and feature at least two distinct limit cycles. Implications for the coexistence of competing populations are discussed. © 2003 Elsevier Science Inc. All rights reserved.

Author-supplied keywords

  • Competitive coexistence
  • Continuous culture
  • Multiple limit cycles
  • Subcritical Hopf bifurcation
  • Variable yield model

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Authors

  • Sergei S. Pilyugin

  • Paul Waltman

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