Transit times and mean ages for nonautonomous and autonomous compartmental systems

被引：0
作者：
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
机构：
[1] Imperial College London,Department of Mathematics
[2] University of California,Department of Environmental Science and Policy
[3] Computational Science Laboratory,Department of Ecology and Evolutionary Biology
[4] Microsoft Research,Department of Mathematics
[5] University of Kansas,Department of Microbiology and Plant Biology
[6] University of Texas,Department of Mathematics
[7] Climate Change Science Institute,undefined
[8] Oak Ridge National Laboratory,undefined
[9] University of Oklahoma,undefined
[10] Microbiology,undefined
[11] Biological Sciences Division,undefined
[12] Pacific Northwest National Laboratory,undefined
[13] University of Oklahoma,undefined
[14] CSIRO Oceans and Atmosphere,undefined
来源：
Journal of Mathematical Biology | 2016年 / 73卷
关键词：
Carbon cycle; CASA model; Compartmental system ; Exponential stability; Linear system; McKendrick–von Förster equation; Mean age; Nonautonomous dynamical system; Transit time; 34A30; 34D05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：1379 / 1398
页数：19
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