We consider the lifting bifurcation problem in the theory of coupled cell networks. Assuming that a steady-state or Hopf bifurcation occurs for a coupled cell system consistent with the structure of a regular network, it is well known that some lifts exhibit new bifurcating branches of solutions. Besides, these additional branches are associated with the increase of the multiplicity of certain eigenvalues, from the quotient adjacency matrix to the lift adjacency matrix. We are so lead to the study of extra eigenvalues in lifts.

We study this lifting bifurcation problem singling out a class of special lifts—the direct lifts. The architectural features of this special class of lifts are investigated.

We also study bifurcations in homogeneous networks.