Global Analysis of Beddington-DeAngelis Type Chemostat Model with Nutrient Recycling and Impulsive Input

Mehbuba Rehim, Lingling Sun, Ahmadjan Muhammadhaji

College of Mathematics and System Sciences, Xinjiang University, Urumqi, China.

DOI: 10.4236/am.2013.48148                

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.

Keywords

Beddington-DeAngelis Model; Chemostat Model; Nutrient Recycling; Global Attractivity

Conflicts of Interest

The authors declare no conflicts of interest.

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