SIFAT-SIFAT SPEKTRAL DAN STRUKTUR KOMBINATORIK PADA SISTEM POSITIF 2D

MATAKUPAN, RUDY WOLTER

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 5 No 1 (2011): BAREKENG : Jurnal Ilmu Matematika dan Terapan

The dynamics of a 2D positive system depends on the pair of nonnegative square matrices thatprovide the updating of its local states. In this paper, several spectral properties, like finitememory, separablility and property L, which depend on the characteristic polynomial of thepair, are investigated under the nonnegativity constraint and in connection with thecombinatorial structure of the matrices.Some aspects of the Perron-Frobenius theory are extended to the 2D case; in particular,conditions are provided guaranteeing the existence of a common maximal eigenvector for twononnegative matrices with irreducible sum. Finally, some results on 2D positive realizationsare presented