Robustness of local adaptive synchronization strategies to topological variations and delays

This paper discusses the robustness properties of a novel decentralized strategy for synchronization of complex networks based on adaptive local gains. Namely, the strategy assumes that each vertex adaptively selects the coupling strength with all of its local neighbours. The strategy was proved to guarantee synchronization and it is shown here to be surprisingly robust to topological variations of the underlying network. The case of time-delays on the coupling between oscillators in the network is also considered showing that, under certain conditions, the strategy still guarantees that the network will synchronize. The observations are supported by numerical simulations on the representative case of networks of Chua's circuits.