Tokyo/Formulation/4.population model

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次に，個体数をN個体にした式で表してみる．
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''' back to [[Tokyo/Works/Simulation |Simulation]]'''
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また，AHLは細胞膜をfreelyに透過と論文に記載あり．よって，細胞の中と外のAHLは同じとした．
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<br>
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Next, to consider the number of cells, the differential equations for multiple cells were given as
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Next, introduce the equation with the number of the cells expressed as n.
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<br>[[Image:expression4-1.jpg|400px|none|thumb|Ex4-1]]
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Here the concentration of AHL is assumed the same inside and outside of a cell according to the description that AHL is freely permiable through cell membrane in the referenced article.  
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where N indicates the number of the cells.
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<br>[[Image:expression4-1.jpg|400px|]]
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<br>In the steady state,time derivatives are zero.As a result,the nullclines of this system were derived as
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<br>ここでもこれまでと同様相平面解析を行う．その際，N個体中の１個体に着目して相平面解析を行う.
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<br>[[Image:expression4-2.jpg|400px|none|thumb|Ex4-2]]
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and then substitute the third equation into the second equation.The nullclines of this system were derived as
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<br>定常状態では，
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<br>[[Image:expression7.JPG|400px|none|thumb|Ex4-3]]
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<br>Analyze the phaseplane with the focus on an individual among n cells.
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<br>In the steady state,
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[[Image:parameter4-1.jpg|right|thumb|150px|Table4-1]]
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<br>To analyze the equations, the values of parameters in the right table were used.The phase plane are shown in Fig●
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<br>[[Image:expression4-2.jpg|400px|]]
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<br>
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-->
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<br>となり，3番目の式を2番目の式に代入する．
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''' back to [[Tokyo/Works/Simulation |Simulation]]'''
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<br>and then substitute the third equation into the second
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== ==
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[[Image:parameter4-1.jpg|thumb|150px|]]
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<br>[[Image:expression4-3.jpg|400px|]]
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<br>パラメータは右の表の値を用いた．相平面解析を行った結果，
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<br>The aprameter were determined by the values in the right table. The result of the phaseplane analysis,
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Latest revision as of 01:56, 27 October 2007

back to Simulation


Next, to consider the number of cells, the differential equations for multiple cells were given as


Ex4-1

where N indicates the number of the cells.


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


Ex4-2

and then substitute the third equation into the second equation.The nullclines of this system were derived as


Ex4-3

back to Simulation

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