Hopf bifurcation analysis for the model of the chemostat with one species of organism. (English) Zbl 1272.92040

Summary: We consider the dynamics of the chemostat model with time delay. The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. By using normal form theory and the center manifold method, we derive the explicit formulas determining the stability and direction of bifurcating periodic solutions. Finally, some numerical simulations are given to illustrate the effectiveness of our results.


92D25 Population dynamics (general)
34C23 Bifurcation theory for ordinary differential equations
37N25 Dynamical systems in biology
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