Tokyo/Formulation/4.population model

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<br>[[Tokyo/Works|Works top]]　　0.[[Tokyo/Works/Hybrid promoter|Hybrid promoter]]　　1.[[Tokyo/Works/Formulation |Formulation]]　　2.[[Tokyo/Works/Assay |Assay1]]　　'''3.[[Tokyo/Works/Simulation |Simulation]]'''　　4.[[Tokyo/Works/Assay2 |Assay2]]　　5.[[Tokyo/Works/Future works |Future works]]
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''' back to [[Tokyo/Works/Simulation |Simulation]]'''
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<br><br>[[Tokyo/Formulation/1.toggle model |Step1]]　　[[Tokyo/Formulation/2.toggle model with hybrid promoter |Step2]]　　[[Tokyo/Formulation/3.AHL-experssing model|Step3]]　　[[Tokyo/Formulation/4.population model|Step4]]　　[[Tokyo/Formulation/5.stochastic differential equation model with poisson random variables|Step5]]
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Next, to consider the number of cells, the differential equations for multiple cells were given as
Next, to consider the number of cells, the differential equations for multiple cells were given as
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<br>[[Image:expression4-2.jpg|400px|none|thumb|Ex4-2]]
<br>[[Image:expression4-2.jpg|400px|none|thumb|Ex4-2]]
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and then substitute the third equation into the second
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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>[[Image:expression7.JPG|400px|none|thumb|Ex4-3]]
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<br>[[Image:expression4-3.jpg|400px|none|thumb|Ex4-3]]
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<!--
[[Image:parameter4-1.jpg|right|thumb|150px|Table4-1]]
[[Image:parameter4-1.jpg|right|thumb|150px|Table4-1]]
<br>To analyze the equations, the values of parameters in the right table were used.The phase plane are shown in Fig●
<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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''' back to [[Tokyo/Works/Simulation |Simulation]]'''
== ==
== ==
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[[Tokyo/Formulation/4.population_model|Step.4]] >> [[Tokyo/Formulation/5.stochastic differential equation model with poisson random variables|Step.5]]
 

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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