Transit times and mean ages for nonautonomous and autonomous compartmental systems
In this study, 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.
- Authors:
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[1]
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; [3]
; [4]
; [5]
; [6]
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- Imperial College London, London (United Kingdom)
- Univ. of California, Davis, CA (United States)
- Microsoft Research, Cambridge (United Kingdom)
- Univ. of Kansas, Lawrence, KS (United States)
- Univ. of Texas, Arlington, TX (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Univ. of Oklahoma, Norman, OK (United States)
- Univ. of Oklahoma, Norman, OK (United States); Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- CSIRO Oceans and Atmosphere, Aspendale, VIC (Australia)
- Publication Date:
- Grant/Contract Number:
- EP/I004165/1; W911NF-13-1-0305; AC05-00OR22725
- Type:
- Accepted Manuscript
- Journal Name:
- Journal of Mathematical Biology
- Additional Journal Information:
- Journal Volume: 73; Journal Issue: 6-7; Journal ID: ISSN 0303-6812
- Publisher:
- Springer
- Research Org:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org:
- USDOE Office of Science (SC)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; carbon cycle; CASA model; compartmental system; exponential stability; linear system; McKendrick-von Forster equation; mean age; nonautonomous; dynamical system; transit time; McKendrick–von Förster equation; nonautonomous dynamical system
- OSTI Identifier:
- 1251563
- Alternate Identifier(s):
- OSTI ID: 1327769
Rasmussen, Martin, Hastings, Alan, Smith, Matthew J., Agusto, Folashade B., Chen-Charpentier, Benito M., Hoffman, Forrest M., Jiang, Jiang, Todd-Brown, Katherine E. O., Wang, Ying, Wang, Ying -Ping, and Luo, Yiqi. Transit times and mean ages for nonautonomous and autonomous compartmental systems. United States: N. p.,
Web. doi:10.1007/s00285-016-0990-8.
Rasmussen, Martin, Hastings, Alan, Smith, Matthew J., Agusto, Folashade B., Chen-Charpentier, Benito M., Hoffman, Forrest M., Jiang, Jiang, Todd-Brown, Katherine E. O., Wang, Ying, Wang, Ying -Ping, & Luo, Yiqi. Transit times and mean ages for nonautonomous and autonomous compartmental systems. United States. doi:10.1007/s00285-016-0990-8.
Rasmussen, Martin, Hastings, Alan, Smith, Matthew J., Agusto, Folashade B., Chen-Charpentier, Benito M., Hoffman, Forrest M., Jiang, Jiang, Todd-Brown, Katherine E. O., Wang, Ying, Wang, Ying -Ping, and Luo, Yiqi. 2016.
"Transit times and mean ages for nonautonomous and autonomous compartmental systems". United States.
doi:10.1007/s00285-016-0990-8. https://www.osti.gov/servlets/purl/1251563.
@article{osti_1251563,
title = {Transit times and mean ages for nonautonomous and autonomous compartmental systems},
author = {Rasmussen, Martin and Hastings, Alan and Smith, Matthew J. and Agusto, Folashade B. and Chen-Charpentier, Benito M. and Hoffman, Forrest M. and Jiang, Jiang and Todd-Brown, Katherine E. O. and Wang, Ying and Wang, Ying -Ping and Luo, Yiqi},
abstractNote = {In this study, 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.},
doi = {10.1007/s00285-016-0990-8},
journal = {Journal of Mathematical Biology},
number = 6-7,
volume = 73,
place = {United States},
year = {2016},
month = {4}
}
- Free Publicly Accessible Full Text
-
Accepted Manuscript (DOE)
- Publisher's Version of Record
- https://doi.org/10.1007/s00285-016-0990-8