Tokyo/Formulation/3.AHL-experssing model

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<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]]
<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]]
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[[Tokyo/Formulation/3.AHL-experssing model|Step.3]] >> [[Tokyo/Formulation/4.population_model|Step.4]]

Revision as of 03:53, 25 October 2007


The differential equaitons of the system considering AHL produced by E.coli themselves were given as


Ex 3-1
Table 3


These equations were normalized as follows:


Ex 3-2


In the steady state,time derivatives are zero.As a result,the nullclines of this system were derived as


Ex 3-3


By substituting the third equation into the second,the nullclines for Ra and Rb were obtained as


Ex 3-4


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:


Figure 3.1.A
Figure 3.1.B
Figure 3.1.C

Step.3 >> Step.4

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