Bifurcation analysis of a chemostat model with two distributed delays
The article studies a chemostat-type model, a system of delay differential equations (DDEs) with two distributed delays as proposed by \textit{E. Beretta} and \textit{Y. Takeuchi} [Differ. Equ. Dyn. Syst. 2, No. 4, 263--288 (199; Zbl 0995.34068)]. The paper proves that the model undergoes a Hopf bifurcation when the average time delay is varied as a bifurcation parameter. The bifurcation is shown to occur for the special case of exponential kernels in the distributed delay terms, which allows a reduction of the DDE system to a system of ordinary differential equations. This result disproves the main statement of \textit{H. A. Abdallah} [Chaos Solitons Fractals 17, No. 5, 879--884 (2003; Zbl 1033.92032)].
scientific article; zbMATH DE number 2093186