Team:ETH Zurich/Modeling/Analytical Approximation
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Revision as of 17:50, 27 October 2011
Analytical Approximation
GFP Band: Dimensionless Model
1. Dimensionless Species
We nondimensionalized all species occurring in the equations for the GFP band circuit.
2. Dimensionless Equations
The dimensionless equations for the dynamics of the band-generating system then read
3. Steady State
4. Dimensionless Groupings
The equation system can be simplified by introducing the following dimensionless groupings:
This yields the final equations for steady state:
Gradient Approximation
Kolmogorov-Petrovsky-Piskounov Equation
Dead Zone Concept
Analytical Solution
References