ON THE SPECTRAL AND COMBINATORIAL STRUCTURE OF 2D POSITIVE SYSTEMS

The dynamics of a 2D positive system depends on the pair of nonnegativ e square matrices that provide the updating of its local states. In th is paper, several spectral properties, such as finite memory, separabi lity, and property L, which depend on the characteristic polynomial of the pair, are investigated under the nonnegativity constraint and in connection with the combinatorial structure of the matrices. Some aspe cts of the Perron-Frobenius theory are extended to the 2D case; in par ticular, conditions are provided guaranteeing the existence of a commo n maximal eigenvector for two nonnegative matrices with irreducible su m. Finally, some results on 2D positive realizations are presented.