This paper studies the existence of Hopf bifurcation for a chemostat model with complementary nutrients and two different delays. Firstly, a four dimension system is reduced to a two dimension system by Lyapunov function and limit set theory. Afterwards, according to the different cases of the delays, respectively, the influence of delays on the dynamic behaviors of the system is discussed, the sufficient conditions are obtained for the stability of the positive equilibrium and the existence of Hopf bifurcation in this system. Finally, some numerical simulations are carried out to verify the theoretical results in this paper.
Key words
chemostat /
delays /
Hopf bifurcation /
stability
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References
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