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Title: 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:
 [1] ;  [2] ;  [3] ;  [4] ;  [5] ;  [6] ;  [7] ;  [8] ;  [7] ;  [9] ;  [7]
  1. Imperial College London, London (United Kingdom)
  2. Univ. of California, Davis, CA (United States)
  3. Microsoft Research, Cambridge (United Kingdom)
  4. Univ. of Kansas, Lawrence, KS (United States)
  5. Univ. of Texas, Arlington, TX (United States)
  6. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  7. Univ. of Oklahoma, Norman, OK (United States)
  8. Univ. of Oklahoma, Norman, OK (United States); Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
  9. CSIRO Oceans and Atmosphere, Aspendale, VIC (Australia)
Publication Date:
OSTI Identifier:
1251563
Grant/Contract Number:
EP/I004165/1; W911NF-13-1-0305
Type:
Accepted Manuscript
Journal Name:
Journal of Mathematical Biology
Additional Journal Information:
Journal Name: Journal of Mathematical Biology; Journal ID: ISSN 0303-6812
Publisher:
Springer
Research Org:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Org:
USDOE
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