Journal
JOURNAL OF MATHEMATICAL BIOLOGY
Volume 73, Issue 6-7, Pages 1379-1398Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-016-0990-8
Keywords
Carbon cycle; CASA model; Compartmental system; Exponential stability; Linear system; McKendrick-von Forster equation; Mean age; Nonautonomous dynamical system; Transit time
Categories
Funding
- EPSRC Career Acceleration Fellowship [EP/I004165/1]
- European Union [643073]
- Army Research Office [W911NF-13-1-0305]
- Biogeochemistry-Climate Feedbacks Scientific Focus Area - Regional and Global Climate Modeling Program in the Climate and Environmental Sciences Division of the Biological and Environmental Research Program in the U.S. Department of Energy Office
- Oak Ridge National Laboratory [DE-AC05-00OR22725]
- U.S. Department of Energy
- Linus Pauling Distinguished Postdoctoral Fellowship program - Laboratory Directed Research and Development Program at Pacific Northwest National Laboratory
- Ralph E. Powe Junior Faculty Enhancement Award from Oak Ridge Associated Universities
- Research Council and College of Arts and Sciences of the University of Oklahoma Norman Campus
- U.S. Department of Energy [DE-SC0006982, DE-SC0008270, DE-SC0014062, DE-SC0004601, DE-SC0010715]
- U.S. National Science Foundation (NSF) [DBI 0850290, EPS 0919466, DEB 0840964, EF 1137293]
- National Science Foundation
- US Department of Homeland Security
- US Department of Agriculture through NSF [EF-0832858]
- University of Tennessee, Knoxville
- Direct For Biological Sciences
- Div Of Biological Infrastructure [1300426] Funding Source: National Science Foundation
- EPSRC [EP/I004165/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/I004165/1] Funding Source: researchfish
- U.S. Department of Energy (DOE) [DE-SC0014062, DE-SC0008270, DE-SC0006982, DE-SC0010715] Funding Source: U.S. Department of Energy (DOE)
Ask authors/readers for more resources
We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick-von Forster 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
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available
Share Paper
