ABSTRACT
Models of the terrestrial carbon cycle are particular cases of compartmental dynamical systems, which are systems of differential equations that must conserve mass. This chapter introduces the main mathematical properties of compartmental dynamical systems and proposes a classification scheme that is useful for the analysis of carbon cycle models. This classification scheme distinguishes between models where carbon inputs and rates change over time or remain constant (nonautonomous versus autonomous models), and between models in which the amount of mass in compartments interact with mass in other compartments (nonlinearity). We show that simple concepts, such as steady state, may not be well defined for some groups of models, and present alternative concepts such as the pullback attractor for the analysis of models with no steady state. In addition, this chapter introduces the theoretical basis for the mathematical analysis of models written in matrix form.
