Concerning the lattice of a network synchrony subspaces, results were obtained concerning: (i) The analysis of  the changes of the lattice that are caused by structural changes in the network topology (deletion and addition of cells or edges, and rewirings of edges); (ii) The characterization of the synchrony subspaces for feed-forward and auto-regulation feed-forward neural networks; (iii) The relation between a network and its fundamental network. 

Concerning network dynamcis, by combining coupled cell networks via the graphs join operation, it is proposed a method of combining coupled cell systems to get dynamics supporting robust simple heteroclinic networks given by the product of robust simple heteroclinic networks (cycles).