Tokyo/Formulation/5.stochastic differential equation model with poisson random variables
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<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. | <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. | ||
- | <br>Next,the relation between the results of simulation and phase plane are shown in Fig.5.4.where nullclines | + | <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]] |
- | + | ||
[[Image:phase plane and simulation-1.JPG|270px|left|thumb|Figure 5.4.1]] | [[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-2.7.JPG|270px|left|thumb|Figure 5.4.2]] |
Revision as of 15:42, 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.
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
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.