Yujiang Liu, Shujing Gao, Shuixian Yan, Fumin Zhang
Key Laboratory of Jiangxi Province for Numerical Simulation
and Emulation Techniques
Gannan Normal University
Ganzhou, 341000, P.R. CHINA

Abstract. A delayed chemostat model with impulsive perturbation on the nutrient concentration and a general nutrient uptake function is considered. The nutrient conversion process involves time delay. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact microorganism-eradication periodic solution of the model and prove the microorganism-eradication periodic solution is globally attractive, provided that the amount of impulsive substrate is less than some critical value. When the amount of impulsive substrate is larger than some critical value, the system is permanent. Computer simulations illustrate the results.

Received: November 3, 2010

AMS Subject Classification: 34A37, 34C25

Key Words and Phrases: chemostat model, delay, impulsive input, permanence

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