From 2007.igem.org

次に，個体数をN個体にした式で表してみる．

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．

Next, introduce the equation with the number of the cells expressed as n. 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.

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.

定常状態では，

Analyze the phaseplane with the focus on an individual among n cells.
In the steady state,

となり，3番目の式を2番目の式に代入する．
and then substitute the third equation into the second

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，
The aprameter were determined by the values in the right table. The result of the phaseplane analysis,