Tokyo/Formulation/3.AHL-experssing model
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<br>The differential equaitons of the system considering AHL produced by E.coli themselves were given as | <br>The differential equaitons of the system considering AHL produced by E.coli themselves were given as | ||
| - | <br> [[Image:expression3-4.jpg|400px|]][[Image:parameter3-1.jpg|200px|]] | + | <br> [[Image:expression3-4.jpg|400px|left|thumb|Ex 3-1]][[Image:parameter3-1.jpg|200px|none|thumb|Table 3]] |
<br>These equations were normalized as follows: | <br>These equations were normalized as follows: | ||
| - | <br>[[Image:expression3-1.jpg|300px|]] | + | <br>[[Image:expression3-1.jpg|300px|none|thumb|Ex 3-2]] |
<br>In the steady state,time derivatives are zero.As a result,the nullclines of this system were derived as | <br>In the steady state,time derivatives are zero.As a result,the nullclines of this system were derived as | ||
| - | <br>[[Image:expression3-2.jpg|300px|]] | + | <br>[[Image:expression3-2.jpg|300px|none|thumb|Ex 3-3]] |
<br>By substituting the third equation into the second,the nullclines for Ra and Rb were obtained as | <br>By substituting the third equation into the second,the nullclines for Ra and Rb were obtained as | ||
| - | <br>[[Image:expression3-3.jpg|300px|]] | + | <br>[[Image:expression3-3.jpg|300px|none|thumb|Ex 3-4]] |
<br>Therefore, the phase plane of this system can be plotted as Fig● and the number of equilibrium points were decided by the value of the parameters: | <br>Therefore, the phase plane of this system can be plotted as Fig● and the number of equilibrium points were decided by the value of the parameters: | ||
| - | <br>[[Image:Phaseplane3-1.jpg|300px|]] [[Image:Phaseplane3-2.jpg| | + | <br>[[Image:Phaseplane3-1.jpg|300px|left|thumb|Figure 3.1.A]] [[Image:Phaseplane3-2.jpg|290px|left|thumb|Figure 3.1.B]] [[Image:Phaseplane3-3.jpg|270px|none|thumb|Figure 3.1.C]] |
Revision as of 05:10, 24 October 2007
The differential equaitons of the system considering AHL produced by E.coli themselves were given as
These equations were normalized as follows:
In the steady state,time derivatives are zero.As a result,the nullclines of this system were derived as
By substituting the third equation into the second,the nullclines for Ra and Rb were obtained as
Therefore, the phase plane of this system can be plotted as Fig● and the number of equilibrium points were decided by the value of the parameters:
