Transit times and mean ages for nonautonomous and autonomous compartmental systems
Journal Article
·
· Journal of Mathematical Biology
We develop a theory for residence times and mean ages for nonautonomous compartmental systems. Using the McKendrick–von Forster 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 residence time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory is consistent with the autonomous case. We apply these results to study a nine-dimensional nonautonomous compartmental system modeling the carbon cycle, which is a simplified version of the Carnegie–Ames–Stanford approach (CASA) model.
- Research Organization:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-76RL01830
- OSTI ID:
- 1333444
- Report Number(s):
- PNNL-SA-114617
- Journal Information:
- Journal of Mathematical Biology, Vol. 73, Issue 6-7; ISSN 0303-6812
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
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