Abstract
In this paper, a chemostat model with periodically pulsed input and time delay is considered. We show that there exists a microorganism-free periodic solution, which is globally attractive when the period of impulsive effect is less than some critical value. Further, we give the sufficient conditions for the permanence of the model with time delay and pulsed input. We show that time delay, impulsive input can bring different effects on the dynamic behavior of the model by numerical analysis. We show that impulsive effect destroys the equilibria of the unforced continuous system and initiates periodic solution. Our results can be applied to culture the microorganism.
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This work is supported by the National Natural Science Foundation of China (No. 10971001) and Henan Science and Technology Department (No. 082102140025 and 092300410228).
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Zhao, Z., Zhang, X. & Chen, L. Nonlinear modelling of chemostat model with time delay and impulsive effect. Nonlinear Dyn 63, 95–104 (2011). https://doi.org/10.1007/s11071-010-9788-1
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DOI: https://doi.org/10.1007/s11071-010-9788-1