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
Abstract
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.