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The asymptotic behavior of a Chemostat model with Crowley–Martin type functional response and time delays

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Abstract

In this paper, we introduce an improved Chemostat model with Crowley–Martin type functional response and time delays. By constructing Lyapunov functionals, the global asymptotic stability of the equilibria is shown in the case of a single species. The conditions for the global asymptotical stability of the model with time delays are obtained via monotone dynamical systems in the case of two species. Our results demonstrate that the effects of predator interference may result in coexistence of two species.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Yanan University, Yanan, 716000, China

    Qinglai Dong & Mingjuan Sun

  2. Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Wanbiao Ma

Authors
  1. Qinglai Dong
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  2. Wanbiao Ma
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  3. Mingjuan Sun
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Corresponding author

Correspondence to Qinglai Dong.

Additional information

The research is partially supported by NSFC(11071013), the Funds of the construction of high-level university in Shaanxi province (2012SXTS06) and the Funds of Yanan University (YD2012-03)

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Dong, Q., Ma, W. & Sun, M. The asymptotic behavior of a Chemostat model with Crowley–Martin type functional response and time delays. J Math Chem 51, 1231–1248 (2013). https://doi.org/10.1007/s10910-012-0138-z

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  • DOI: https://doi.org/10.1007/s10910-012-0138-z

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