Shigui Ruan

Publications (1)0 Total impact

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  Available from: Gail S.K. Wolkowicz

  Article: Competition In The Chemostat: A Distributed Delay Model And Its Global Asymptotic Behavior

  Gail S. K. Wolkowicz, Huaxing Xia, Shigui Ruan
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  ABSTRACT: . In this paper, we propose a two species competition model in a chemostat that uses a distributed delay to model the lag in the process of nutrient conversion and study the global asymptotic behavior of the model. The model includes a washout factor over the time delay involved in the nutrient conversion and hence the delay is distributed over the species concentrations as well as over the nutrient concentration (using the gamma distribution). The results are valid for a very general class of monotone growth response functions. By using the linear chain trick technique and the Fluctuation Lemma, we completely determine the global limiting behavior of the model and prove that there is always at most one survivor and give a criterion to predict the outcome that is dependent upon the parameters in the delay kernel. We compare these predictions on the qualitative outcome of competition introduced by including distributed delay in the model with the predictions made by the the correspondin...
  06/1997;