Tokyo/Formulation/5.stochastic differential equation model with poisson random variables
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<br>The values of parameters in the right table were used and the results of simulation were shown in Fig 5.1-3. | <br>The values of parameters in the right table were used and the results of simulation were shown in Fig 5.1-3. | ||
<br>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). | <br>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). | ||
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+ | <br>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. | ||
+ | <br>Fig.5.2 indicates that a portion of cells shift to A state and the others shift to B state in steady state;that is,individual cells are stable under stable coexistence. | ||
[[Image:3d-1-0.2.JPG|200px|left|thumb|Figure 5.1.A t=0.2(min)]] | [[Image:3d-1-0.2.JPG|200px|left|thumb|Figure 5.1.A t=0.2(min)]] | ||
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<br>Next,the relation between the results of simulation and phase plane are shown in Fig.5.4.1-3,where the nullclines of this system were [[Tokyo/Formulation/4.population model|Ex 4-3]] | <br>Next,the relation between the results of simulation and phase plane are shown in Fig.5.4.1-3,where the nullclines of this system were [[Tokyo/Formulation/4.population model|Ex 4-3]] |
Revision as of 20:51, 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
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).
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 a portion of cells shift to A state and the others shift to B state in steady state;that is,individual cells are stable under stable coexistence.
movie here!!
movie here!!
movie here!!
Next,the relation between the results of simulation and phase plane are shown in Fig.5.4.1-3,where the nullclines of this system were Ex 4-3
Fig.5.4.1-3 indicate that the distribution of the cells corresponds with the stable equilibrium points.