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Transit times and mean ages for nonautonomous and autonomous compartmental systems
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- Journal Article
- Science & Technology
- Life Sciences & Biomedicine
- Biology
- Mathematical & Computational Biology
- Life Sciences & Biomedicine - Other Topics
- Carbon cycle
- CASA model
- Compartmental system
- Exponential stability
- Linear system
- McKendrick-von Forster equation
- Mean age
- Nonautonomous dynamical system
- Transit time
- CARBON-CYCLE
- SOIL RESPIRATION
- MODEL
- CO2
- DICHOTOMY
- CASA model
- Carbon cycle
- Compartmental system
- Exponential stability
- Linear system
- McKendrick–von Förster equation
- Mean age
- Nonautonomous dynamical system
- Transit time
- Carbon Cycle
- Models, Biological
- Time Factors
- Models, Biological
- Time Factors
- Carbon Cycle
- math.DS
- math.DS
- 34A30, 34D05
- Bioinformatics
- 01 Mathematical Sciences
- 06 Biological Sciences