Analysis of a Crowley-Martin Type Chemostat with Delayed Growth Response and Pulsed Input

2014 ◽  
Vol 556-562 ◽  
pp. 4333-4337
Author(s):  
Ming Juan Sun ◽  
Hua Xin Zhao ◽  
Qing Lai Dong
Keyword(s):  
Differential Equation ◽  
Growth Response ◽  
Global Attractivity ◽  
Computational Techniques ◽  
Chemostat Model ◽  
Delayed Differential Equation ◽  
Delayed Growth

In this paper, we introduce and study a Crowley-Martin type Chemostat model with delayed growth response and pulsed input. We get that the existence and the global attractivity of a ‘microorganism-extinction’periodic solution. We prove that the system is permanent under appropriate conditions, by use of new computational techniques for impulsive and delayed differential equation.

scholarly journals Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Kai Wang ◽  
Zhidong Teng ◽  
Fengqin Zhang
Keyword(s):  
Function Method ◽  
Global Attractivity ◽  
Necessary Conditions ◽  
Nutrient Recycling ◽  
Liapunov Function ◽  
Sufficient Condition ◽  
Chemostat Model ◽  
Dynamic Behaviors ◽  
Analysis Technique ◽  
Sufficient And Necessary Conditions

The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established. Finally, an example is given to demonstrate the effectiveness of the results in this paper.

Sign in / Sign up

Export Citation Format

Share Document