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dc.contributor.authorRasmussen, Martin
dc.contributor.authorHastings, Alan
dc.contributor.authorSmith, Matthew J.
dc.contributor.authorAgusto, Folashade B.
dc.contributor.authorChen-Charpentier, Benito M.
dc.contributor.authorHoffman, Forrest M.
dc.contributor.authorJiang, Jiang
dc.contributor.authorTodd-Brown, Katherine E. O.
dc.contributor.authorWang, Ying
dc.contributor.authorWang, Ying-Ping
dc.contributor.authorLuo, Yiqi
dc.date.accessioned2016-12-01T21:38:57Z
dc.date.available2016-12-01T21:38:57Z
dc.date.issued2016-04-01
dc.identifier.citationTransit 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/s00285-016-0990-8en_US
dc.identifier.urihttp://hdl.handle.net/1808/22113
dc.description.abstractWe 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.publisherSpringer Verlagen_US
dc.rightsCopyright © 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.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectCarbon cycleen_US
dc.subjectCASA modelen_US
dc.subjectCompartmental systemen_US
dc.subjectExponential stabilityen_US
dc.subjectLinear systemen_US
dc.subjectMcKendrick-von Forster equationen_US
dc.subjectMean ageen_US
dc.subjectNonautonomous dynamical systemen_US
dc.subjectTransit timeen_US
dc.titleTransit times and mean ages for nonautonomous and autonomous compartmental systemsen_US
dc.typeArticleen_US
kusw.kuauthorAgusto, Folashade B.
kusw.kudepartmentEcology & Evolutionary Biologyen_US
dc.identifier.doi10.1007/s00285-016-0990-8
kusw.oaversionScholarly/refereed, publisher versionen_US
kusw.oapolicyThis item meets KU Open Access policy criteria.en_US
dc.rights.accessrightsopenAccess


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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.
Except where otherwise noted, this item's license is described as: 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.