Dynamical behavior of 2D positive systems

In the paper the definition and main properties of a 2-digraph, i.e. a directed graph with two kinds of arcs, are introduced. Natural constrains on the com-position of the paths connecting each pair of vertices lead to the definition of 2-strongly connected digraph and of 2-imprimitivity classes. Irreducible matrix pairs, that is pairs endowed with a 2-strongly connected digraph, are subsequently dis-cussed. Equivalent descriptions of irreducibility, re-ferring to the free evolution of the 2D state models described by the pairs and to their characteristic poly-nomials, are provided. Finally, primitivity, viewed as a special case of irreducibility, is introduced and char-acterized.