The effects of delayed growth response on the dynamic behaviors of the Monod type chemostat model with impulsive input nutrient concentration

2010 ◽  
Vol 11 (5) ◽  
pp. 4476-4486 ◽  
Author(s):  
Xinzhu Meng ◽  
Qian Gao ◽  
Zhenqing Li
Keyword(s):  
Nutrient Concentration ◽  
Growth Response ◽  
Chemostat Model ◽  
Dynamic Behaviors ◽  
Impulsive Input ◽  
Delayed Growth

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.

scholarly journals A distinct growth physiology enhances bacterial growth under rapid nutrient fluctuations

2020 ◽  
Author(s):  
Jen Nguyen ◽  
Vicente Fernandez ◽  
Sammy Pontrelli ◽  
Uwe Sauer ◽  
Martin Ackermann ◽  
...  
Keyword(s):  
Growth Rate ◽  
Bacterial Growth ◽  
Nutrient Concentration ◽  
Growth Response ◽  
Average Concentration ◽  
Growth Physiology ◽  
E Coli ◽  
Growth Loss ◽  
Concentration Characteristic ◽  
Cell Microscopy

AbstractIt has been long known that bacteria coordinate their physiology with environmental nutrient, yet our current understanding offers little intuition for how bacteria respond to the second-to-minute scale fluctuations in nutrient concentration characteristic of many microbial habitats. To investigate the effects of rapid nutrient fluctuations on bacterial growth, we coupled custom microfluidics with single-cell microscopy to quantify the growth rate of E. coli experiencing 30 s to 60 min nutrient fluctuations. Compared to steady environments of equal average concentration, fluctuating environments reduced growth rate by up to 50%. However, measured reductions in growth rate were only 38% of the growth loss predicted from single nutrient shifts — an enhancement produced by the distinct growth response of cells grown in environments that fluctuate rather than shift once. We report an unexpected physiology adapted for growth in nutrient fluctuations and implicate nutrient timescale as a critical environmental parameter beyond nutrient concentration and source.

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