Qualitative analysis of a model for co-culture of bacteria and amoebae

  • Received: 01 February 2011 Accepted: 29 June 2018 Published: 01 March 2012
  • MSC : 37L10, 92D25.

  • In this article we analyze a mathematical model presented in [11]. The model consists of two scalar ordinary differential equations, which describe the interaction between bacteria and amoebae. We first give the sufficient conditions for the uniform persistence of the model, then we prove that the model can undergo Hopf bifurcation and Bogdanov-Takens bifurcation for some parameter values, respectively.

    Citation: Laura Fumanelli, Pierre Magal, Dongmei Xiao, Xiao Yu. Qualitative analysis of a model for co-culture of bacteria and amoebae[J]. Mathematical Biosciences and Engineering, 2012, 9(2): 259-279. doi: 10.3934/mbe.2012.9.259

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  • In this article we analyze a mathematical model presented in [11]. The model consists of two scalar ordinary differential equations, which describe the interaction between bacteria and amoebae. We first give the sufficient conditions for the uniform persistence of the model, then we prove that the model can undergo Hopf bifurcation and Bogdanov-Takens bifurcation for some parameter values, respectively.
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    © 2012 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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