Pinning controllability of asymmetrical weighted scale-free networks

This letter studies the pinning controllability of asymmetrical weighted scale-free networks, in which every individual node is a chaotic Lorenz system. The selective pinning scheme, which gives the control priority to those nodes with largest numbers of connections, is adopted. Study shows that a dynamical network of this type can be controlled via selective pinning only when the proportion p of the controlled nodes exceeds a critical value p_c; and the network pinning controllability is enhanced as p increases for p >p_c. This study also reveals the effects of the weights and the topologies of this type of networks on their pinning controllability, showing that pinning controllability of a network can be improved with an asymmetrical weight distribution, where the couplings from older nodes to younger ones are dominant, with a larger average connectivity or with a more heterogeneous connection distribution.