Synchronization of complex networks through local adaptive coupling

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 presented in the paper is shown via two representative examples: adaptive consensus and the adaptive synchronization of a network on N coupled Chua's circuits.