Tokyo/Formulation/4.population model

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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, to consider the number of cells, the differential equations for multiple cells were given as
<br>[[Image:expression4-1.jpg|400px|]]
<br>[[Image:expression4-1.jpg|400px|]]

Revision as of 16:26, 23 October 2007

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


Expression4-1.jpg


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


Expression4-2.jpg


and then substitute the third equation into the second

Parameter4-1.jpg


Expression4-3.jpg


To analyze the equations, the values in the right table were used.The phase plane are shown in Fig●