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 |
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CompartmentalSystems.smooth_model_run |
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CompartmentalSystems.start_distributions |
Jupyter notebook examples¶
- Analysis of a nonlinear global carbon cycle model (html)
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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 \(j\)