Synchronization in Complex Hybrid Networks

Synchronization in complex hybrid networks is studied. Hybrid networks presents the so called "small world" phenomenon, i.e. small distance between any pair of nodes and clustering effect, and can be considered as the union of a local and a global graph, the former providing local connections and the latter providing small distances. After recalling a few results stated in previous papers, we prove that although local graph networks do not synchronize when the number N of nodes is large, the addition of only a small number of global edges makes these hybrid networks synchronize. The obtained results are supported by numerical examples.