Two local adaptive strategies for the synchronization of complex networks are discussed in
this paper. One, termed as vertex-based, uses local adaptive coupling gains at each node in
the network. The other, named edge-based, associates to each edge in the network an
adaptive coupling gain, determined solely on the basis of local information. The global
asymptotic stability of the synchronous evolution is proven for both strategies using
appropriate Lyapunov-based techniques. The effectiveness of the adaptive methodologies …