It means the within each universal stage of effectiveness there are several types-attractors that 'attract' societies surviving lost of stability and browsing in the bifurcation zone. From this viewpoint tribes and chiefdoms may be located on the same stage, early states, Greek polisies, confederations of tribes - on the next stage, and so long. In this scheme the tops connected by edges are types-attractors, or more simply, backwaters of stability which attract societies. Chase-Dunn and Th. Each world-system is a hierarchy of societies.
World empires have imperial center, heartland, close and far provinces, merchant cities.
The presented model is by no means a theory but just a wide-scope framework for bridging various paradigms dealing with macrohistorical dynamics, social evolution, and world history periodization. The thesis is that further theoretization of this area must take into account, compare and combine various approaches and paradigms, and the presented 5-levels model of macrohistorical dynamics provides wide possibilities and strict conceptualizations for this promising theoretical work. The Perspective of the World. Carneiro, Robert L. 1970. A Theory of the Origin of the State.