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S. Ruan, “The Effect of Delays on Stability and Persis tence in Plankton Models,” Nonlinear Analysis: Real Word Applications, Vol. 24, No. 4, 1995, pp. 575-585.

has been cited by the following article:

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

  AUTHORS: Mehbuba Rehim, Lingling Sun, Ahmadjan Muhammadhaji

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

  JOURNAL NAME: Applied Mathematics, Vol.4 No.8, July 23, 2013

  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.