| Abstract: |
| We develop a theory for transit times and mean ages for non-autonomous compartmental systems. Using the McKendrick-von Forster equation, we show that the mean ages of mass in a compartmental system satisfy a linear non-autonomous ordinary differential equation that is exponentially stable. We then define a non-autonomous version of transit time as the mean age of mass leaving the compartmental system at a particular time and show that our non-autonomous theory generalizes the autonomous case. We apply these results to study a nine-dimensional non-autonomous compartmental system modeling the terrestrial carbon cycle, which is a modification of the Carnegie-Ames-Stanford approach model, and we demonstrate that the non-autonomous versions of transit time and mean age differ significantly from the autonomous quantities when calculated for that model. |
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