View source for Sensitivity Analysis

;Analysis title
:[[File:Differential-algebraic-equations-Sensitivity-Analysis-icon.png]] Sensitivity Analysis
;Provider
:[[Institute of Systems Biology]]
;Class
:{{Class|biouml.plugins.modelreduction.SensitivityAnalysis}}
;Plugin
:[[Biouml.plugins.modelreduction (plugin)|biouml.plugins.modelreduction (Model reduction plug-in)]]

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

:: [[File: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 ''c''<sup>0</sup>), and ''t'' (time) is the variable of integration.

The local unscaled sensitivities ∂''c''/∂''α<sub>j</sub>'' are calculated via finite difference approximations

:: [[File:Differential-algebraic-equations-Sensitivity-Analysis-sa2.png]]

where ''c<sub>ss</sub>''(''α<sub>j</sub>'') and ''c<sub>ss</sub>''(''α<sub>j</sub>''+Δ''α<sub>j</sub>'') correspond to the solutions of the algebraic systems ''f''(''c'', ''α<sub>j</sub>'') = 0 and ''f''(''c'', ''α<sub>j</sub>''+Δ''α<sub>j</sub>'') = 0 respectively.

The scaled sensitivities is calculated by multiplying each component ∂''c<sup>k</sup>''/∂''α<sub>j</sub>'' of the vector ∂''c''/∂''α<sub>j</sub>'' by the normalization factor ''α<sub>j</sub>''/''c<sup>k</sup><sub>ss</sub>''(''α<sub>j</sub>'').

==== References ====

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

[[Category:Analyses]]
[[Category:Differential algebraic equations (analyses group)]]
[[Category:ISB analyses]]
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