Before revision:  We find strikingly different phase diagrams corresponding to each networkstructure . Neuronal network dynamics is not only different within certain parameter ranges, but it also undergoes different bifurcations . Our results therefore suggest cautiousness when using mean-field models based on all-to-all network topologies to represent random networks .
After revision:  We find strikingly different phase diagrams corresponding to each networkstructure . Neuronal network dynamics is not only different within certain parameter ranges, but it also undergoes different bifurcations (with a richer repertoire of bifurcations in ER and RR compared to all-to-all network topologies to represent random networks .