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Global Analysis of Beddington-DeAngelis Type Chemostat Model with Nutrient Recycling and Impulsive Input
College of Mathematics and System Sciences, Xinjiang University, Urumqi, China
College of Mathematics and System Sciences, Xinjiang University, Urumqi, China
College of Mathematics and System Sciences, Xinjiang University, Urumqi, China
- 1 College of Mathematics and System Sciences, Xinjiang University, Urumqi, China
- 2 College of Mathematics and System Sciences, Xinjiang University, Urumqi, China
- 3 College of Mathematics and System Sciences, Xinjiang University, Urumqi, China
Applied Mathematics·Volume 04 (2013)·Pages 1097–1105·Published 23 July 2013·DOI10.4236/am.2013.48148
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Abstract
In this paper, a Beddington-DeAngelis type chemostat model with nutrient recycling and impulsive input is considered. Except using Floquet theorem, introducing a new method combining with comparison theorem of impulse differential equation and by using the Liapunov function method, the sufficient and necessary conditions on the permanence and extinction of the microorganism are obtained. Two examples are given in the last section to verify our mathematical results. The numerical analysis shows that if only the system is permanent, then it also is globally attractive.
KeywordsBeddington-DeAngelis ModelChemostat ModelNutrient RecyclingGlobal Attractivity
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