Generalized circulant matrix in Coupled Map Lattices

In this paper it is shown that a generalized circulant matrix underlies every weakly Coupled Map Lattice (CML), independently of the form of the coupling term. Therefore, this matrix will appear always perturbative methods are used to get the analytical solutions. In fact, the inverse of this matrix provides the analytical solution of the CML after using first order approximation methods. This inverse matrix, of arbitrary order, is explicitly calculated, thus providing the analytical expression for the temporal evolution of the CML.