Sensitivity Analysis

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Analysis title
Differential-algebraic-equations-Sensitivity-Analysis-icon.png Sensitivity Analysis
Provider
Institute of Systems Biology
Class
SensitivityAnalysis
Plugin
biouml.plugins.modelreduction (Model reduction plug-in)

Description

The method calculates sensitivities associated with the steady state of the purely temporal system

Differential-algebraic-equations-Sensitivity-Analysis-sa1.png

where c is the n-vector of species concentrations, α is the m-vector of systems parameters (which can include the initial conditions c0), and t (time) is the variable of integration.

The local unscaled sensitivities ∂c/∂αj are calculated via finite difference approximations

Differential-algebraic-equations-Sensitivity-Analysis-sa2.png

where css(αj) and css(αjαj) correspond to the solutions of the algebraic systems f(c, αj) = 0 and f(c, αjαj) = 0 respectively.

The scaled sensitivities is calculated by multiplying each component ∂ck/∂αj of the vector ∂c/∂αj by the normalization factor αj/ckss(αj).

References

  1. H Rabitz, M Kramer, D Dacol, "Sensitivity analysis in chemical kinetics". Annu. Rev. of Phys. Chem., 34:419-461.
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