Compartmental Systems¶
CompartmentalSystems is a Python package to deal with compartmental models of the form
\[\frac{d}{dt}\,x(t) = B(x(t),t)\,x(t) + u(t).\]
Since most computations are based on the state transition operator \(\Phi\) that solves
\[\frac{d}{dt}\,\Phi(t,s) = B(t)\,\Phi(t,s),\quad \Phi(s,s) = \bf{I},\]
nonlinear models need to be linearized in the first step. Then the package provides numerical computation of
age
 compartmental age densities
 system age densities
 compartmental age mean and higher order moments
 system age mean and higher order moments
 compartmental age quantiles
 system age quantiles
transit time
 forward and backward transit time densities
 backward transit time mean and higher order moments
 forward and backward transit time quantiles
Table of Contents¶
CompartmentalSystems.smooth_reservoir_model 

CompartmentalSystems.smooth_model_run 

CompartmentalSystems.start_distributions 
Jupyter notebook examples¶
 Analysis of a nonlinear global carbon cycle model (html)
.
Analysis of a nonlinear global carbon cycle model (ipynb)
Important Note¶
\(B(t)=(b_{ij}(t))\) is supposed to be a compartmental matrix for all times \(t\):
 \(b_{ii}(t)\leq0\) for all \(i\)
 \(b_{ij}(t)\geq0\) for \(i\neq j\)
 \(\sum\limits_{i=1}^d b_{ij}(t)\leq 0\) for all \(j\)