ABSTRACT
The matrix equation model for the terrestrial carbon dynamics is a system of nonautonomous ordinary differential equations, ODEs, which naturally inherits the mathematical difficulties in the solution process and stability studies of its equilibria. This chapter introduces the mathematical properties of this matrix equation model. In particular, we will study: (1) the analytical solution of the matrix equation model, examining a three-pool terrestrial carbon dynamics representation to demonstrate the solution process; and (2) the stability analysis of the matrix equation model.
