Cost and effect of pinning control for network synchronization

The problem of pinning control for the synchronization of complexdynamical networks is discussed in this paper. A cost function ofthe controlled network is defined by the feedback gain and thecoupling strength of the network. An interesting result is that alower cost is achieved by using the control scheme of pinning nodeswith smaller degrees. Some strict mathematical analyses arepresented for achieving a lower cost in the synchronization ofdifferent star-shaped networks. Numerical simulations on somenon-regular complex networks generated by the Barabási--Albertmodel and various star-shaped networks are performed forverification and illustration.