The effects of delayed growth response on the dynamic behaviors of the Monod type chemostat model with impulsive input nutrient concentration

Abstract This paper investigates the effects of delayed growth response on the dynamic behaviors of the Monod type chemostat model with impulsive input nutrient concentration. By the use of the discrete dynamical system determined by the stroboscopic map, we obtain a ‘microorganism-extinction’ periodic solution, further, prove that the ‘microorganism-extinction’ periodic solution is globally attractive if the impulsive period satisfies some conditions. Using the theory on delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the system, and prove that time delays, impulsive input nutrient can bring obvious effects on the dynamic behaviors of the model.

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