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THE DYNAMICS OF A CHEMOSTAT MODEL WITH STATE DEPENDENT IMPULSIVE EFFECTS

LINFEI NIE

College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, P. R. China

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ZHIDONG TENG

College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, P. R. China

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, and

LIN HU

College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, P. R. China

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https://doi.org/10.1142/S0218127411029173Cited by:20 (Source: Crossref)

Abstract

We consider the dynamic behaviors of a mathematical chemostat model with state dependent impulsive perturbations. By using the Poincaré map and analogue of Poincaré's criterion, some conditions for the existence and stability of positive periodic solution are obtained. Moreover, we show that there is no periodic solution with order larger than or equal to three. Numerical simulation are carried out to illustrate the feasibility of our main results, thus implying that the presence of pulses makes the dynamic behavior more complex.

This work was supported by the National Natural Science Foundation of China (Nos. 11001235, 10961022), and the Natural Science Foundation of Xinjiang University (BS100104, BS080105). This work was supported by the National Natural Science Foundation of P. R. China (11001235, 10961022, 60764003), the Major Project of The Ministry of Education of P. R. China (207130), the Scientific Research Programmes of Colleges in Xinjiang (XJEDU2007G01, XJEDU2006I05) and the Natural Science Foundation of Xinjiang University (BS080105).

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