Tokyo/Formulation/3.AHL-experssing model

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<br>[[Image:expression3-1.jpg|300px|]]
<br>[[Image:expression3-1.jpg|300px|]]
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<br>As a result,the nullclines of this system were derived as
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<br>In the steady state,time derivations 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|]]

Revision as of 13:38, 23 October 2007


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


Expression3-4.jpgParameter3-1.jpg


These equations were normalized as follows:


Expression3-1.jpg


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


Expression3-2.jpg


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


Expression3-3.jpg


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:


Phaseplane3-1.jpg Phaseplane3-2.jpg Phaseplane3-3.jpg