Global Qualitative Analysis of a New Monod Type Chemostat Model With Delayed Growth Response and Pulsed Input in a Polluted Environment

MENG Xin-zhu; ZHAO Qiu-lan; CHEN Lan-sun

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(1): 69-80

MENG Xin-zhu, ZHAO Qiu-lan, CHEN Lan-sun. Global Qualitative Analysis of a New Monod Type Chemostat Model With Delayed Growth Response and Pulsed Input in a Polluted Environment[J]. Applied Mathematics and Mechanics, 2008, 29(1): 69-80.

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Global Qualitative Analysis of a New Monod Type Chemostat Model With Delayed Growth Response and Pulsed Input in a Polluted Environment

1.
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China;

Received Date: 2007-09-05
Rev Recd Date: 2007-12-10
Publish Date: 2008-01-15

Abstract

Abstract

A new Monod type chemostat model is considered with time delay and pulsedinput concentration of the nutrient in a polluted environment. Using the discrete dynamical system deter mined by the stroboscopic map, a-microorg anismex tinction. periodic solution is obtained. Further more, the sufficient conditions for the global attractivity of the micro organism-extinction periodic solution are established. Using new computational techniques for impulsive and delayed differential equation, it is proved that the system is permanent under appropriate conditions. The results show that time delay is "profitless".
- permanence,
- impulsive input,
- chemostat model,
- time delay for growth response,
- extinction

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References(37)

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