Transit times and mean ages for nonautonomous and autonomous compartmental systems
dc.contributor.author | Rasmussen, Martin | |
dc.contributor.author | Hastings, Alan | |
dc.contributor.author | Smith, Matthew J. | |
dc.contributor.author | Agusto, Folashade B. | |
dc.contributor.author | Chen-Charpentier, Benito M. | |
dc.contributor.author | Hoffman, Forrest M. | |
dc.contributor.author | Jiang, Jiang | |
dc.contributor.author | Todd-Brown, Katherine E. O. | |
dc.contributor.author | Wang, Ying | |
dc.contributor.author | Wang, Ying-Ping | |
dc.contributor.author | Luo, Yiqi | |
dc.date.accessioned | 2016-12-01T21:38:57Z | |
dc.date.available | 2016-12-01T21:38:57Z | |
dc.date.issued | 2016-04-01 | |
dc.identifier.citation | Transit times and mean ages for nonautonomous and autonomous compartmental systems Martin Rasmussen, Alan Hastings, Matthew J. Smith, Folashade B. Agusto, Benito M. Chen-Charpentier, Forrest M. Hoffman, Jiang Jiang, Katherine E. O. Todd-Brown, Ying Wang, Ying-Ping Wang, Yiqi Luo J Math Biol. 2016; 73(6): 1379–1398. Published online 2016 Apr 1. doi: 10.1007/s00285-016-0990-8 | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/22113 | |
dc.description.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. | en_US |
dc.publisher | Springer Verlag | en_US |
dc.rights | Copyright © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.subject | Carbon cycle | en_US |
dc.subject | CASA model | en_US |
dc.subject | Compartmental system | en_US |
dc.subject | Exponential stability | en_US |
dc.subject | Linear system | en_US |
dc.subject | McKendrick-von Forster equation | en_US |
dc.subject | Mean age | en_US |
dc.subject | Nonautonomous dynamical system | en_US |
dc.subject | Transit time | en_US |
dc.title | Transit times and mean ages for nonautonomous and autonomous compartmental systems | en_US |
dc.type | Article | en_US |
kusw.kuauthor | Agusto, Folashade B. | |
kusw.kudepartment | Ecology & Evolutionary Biology | en_US |
dc.identifier.doi | 10.1007/s00285-016-0990-8 | |
kusw.oaversion | Scholarly/refereed, publisher version | en_US |
kusw.oapolicy | This item meets KU Open Access policy criteria. | en_US |
dc.rights.accessrights | openAccess |
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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.