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

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Revision as of 14:28, 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

movie here!!

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

movie here!!

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

movie here!!

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

これたの図から相平面上の安定点と大腸菌の分布とが一致しているの分かる．