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

1. Center for Information Technology, Bruno Kessler Foundation, via Sommarive 18, I-38123 Trento Povo
2. Institut de Mathématiques de Bordeaux, UMR CNRS 5251 - Case 36, Université Victor Segalen Bordeaux 2, 3ter place de la Victoire 33076 Bordeaux Cedex
3. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240

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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