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Article Abstract
We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick-von Förster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary differential equation that is exponentially stable. We then define a nonautonomous version of transit time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory generalises the autonomous case. We apply these results to study a nine-dimensional nonautonomous compartmental system modeling the terrestrial carbon cycle, which is a modification of the Carnegie-Ames-Stanford approach model, and we demonstrate that the nonautonomous versions of transit time and mean age differ significantly from the autonomous quantities when calculated for that model.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5061853 | PMC |
| http://dx.doi.org/10.1007/s00285-016-0990-8 | DOI Listing |
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