  Consensus algorithms on networks have received increasing attention in recent
years for various applications ranging from animal flocking to multi-vehicle
co-ordination. Building on the established model for second-order consensus of
multi-agent networks, we uncover a mechanism inhibiting the formation of
collective consensus states via rather small time-periodic coupling
modulations. We treat the model in its spectral decomposition and find
analytically that for certain intermediate coupling frequencies parametric
resonance is induced on a network level -- at odds with the expected emergence
of consensus for very short and long coupling time-scales. Our formalism
precisely predicts those resonance frequencies and links them to the Laplacian
spectrum of the static backbone network. The excitation of the system is
furthermore quantified within the theory of parametric resonance, which we
extend to the domain of networks with time-periodic couplings.
