Enhancing synchronization based on complex gradient networks

The ubiquity of scale-free networks in nature and technological applications and the finding that such networks may be more difficult to synchronize than homogeneous networks pose an interesting phenomenon for study in network science. We argue and demonstrate that, in the presence of some proper gradient fields, scale-free networks can be more synchronizable than homogeneous networks. The gradient structure can in fact arise naturally in any weighted and asymmetrical networks; based on this we propose a coupling scheme that permits effective synchronous dynamics on the network. The synchronization scheme is verified by eigenvalue analysis and by direct numerical simulations using networks of nonidentical chaotic oscillators.