Applied Mathematics and Mechanics

, Volume 29, Issue 1, pp 75–87

# Global qualitative analysis of new Monod type chemostat model with delayed growth response and pulsed input in polluted environment

• Meng Xin-zhu  (孟新柱)
• Zhao Qiu-lan  (赵秋兰)
• Chen Lan-sun  (陈兰荪)
Article

## Abstract

In this paper, we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain a “microorganism-extinction” periodic solution. Further, we establish the sufficient conditions for the global attractivity of the microorganism-extinction periodic solution. Using new computational techniques for impulsive and delayed differential equation, we prove that the system is permanent under appropriate conditions. Our results show that time delay is “profitless”.

## Key words

permanence impulsive input chemostat model time delay for growth response extinction

O175

## 2000 Mathematics Subject Classification

34K45 34C05 92D25

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© Editorial Committee of Appl. Math. Mech. and Springer-Verlag 2008

## Authors and Affiliations

• Meng Xin-zhu  (孟新柱)
• 1
• 2
Email author
• Zhao Qiu-lan  (赵秋兰)
• 1
• Chen Lan-sun  (陈兰荪)
• 2
• 3
1. 1.College of ScienceShandong University of Science and TechnologyQingdaoP. R. China
2. 2.Department of Applied MathematicsDalian University of TechnologyDalianP. R. China
3. 3.Institute of Mathematics, Academy of Mathematics and System SciencesChinese Academy of SciencesBeijingP. R. China