Tokyo/Formulation/5.stochastic differential equation model with poisson random variables

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Revision as of 10:28, 24 October 2007

we introduced the terms of Ex 4-1 into a stochastic process to simulate the sthochastic behavior.we used Poisson random variables as a sthochastic process. Threfore,a stochastic differential equations were given as

Ex 5-1

Table 5

The values of parameters in the right table were used and the results of simulation were shown in Fig 5.1-3.
where α2 = 1(μM) in Fig 5.1,α2 = 2.7(μM) in Fig 5.2,α2 = 4(μM) in Fig 5.3. and it has been estimated that 1(μM) = 1000 molecules (count).

Figure 5.1.A 　t=0.2(min)

Figure 5.1.B 　t=0.8(min)

Figure 5.1.C 　 t=30(min)　　 failure only A

Figure 5.2.A 　t=0.2(min)

Figure 5.2.B 　 t=0.8(min)

Figure 5.2.C 　 t=30(min)　　success!! coexistence

Figure 5.3.A 　 t=0.2(min)

Figure 5.3.B 　 t=0.8(min)

Figure 5.3.C 　 t=30(min)　　 failure only B

Fig.5.1 indicates that all cells shift to A state in the steady state and Fig 5.3 indicates that all cells shift to B state in the steady state.These results doesn't represent coexistence stable.
Fig.5.2 indicates that in the steady state the cells at A state and that at B state Fig.5.2は，AとBに分かれて安定している．

次に，Simulationの結果と相平面の関係を見てみる．相平面のヌルクラインはEx4-3を用いている．

Figure 5.4.1

Figure 5.4.2

Figure 5.4.3

@@ Line 30: / Line 30: @@
 Fig.5.2は，AとBに分かれて安定している．
+<br>次に，Simulationの結果と相平面の関係を見てみる．相平面のヌルクラインはEx4-3を用いている．
 [[Image:phase plane and simulation-1.JPG|270px|left|thumb|Figure 5.4.1]]
 [[Image:phase plane and simulation-2.7.JPG|270px|left|thumb|Figure 5.4.2]]
 [[Image:phase plane and simulation-4.JPG|270px|none|thumb|Figure 5.4.3]]

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Tokyo/Formulation/5.stochastic differential equation model with poisson random variables

From 2007.igem.org

Revision as of 10:28, 24 October 2007