Synchronizability in complex ad hoc dynamical networks with accelerated growth

Recent research works have been pursued in connection with network synchronizability under various constraints for different topological structures and evolving mechanisms. However, the fundamental question of how the synchronizability of the networks relates to accelerated growth and ad hoc property in the evolving processes remains underexplored. Here we study the ad hoc dynamical models with accelerated growth where the total number of edges increases faster than linearly with network size. By adopting three attachment mechanisms: random, rewired, and preferential attachment, we investigate the second-largest eigenvalues and the ratios of the extremal eigenvalues of coupled matrices in the accelerated models with different evolving parameters. For the new models, we demonstrate the robustness and fragility of synchronization against random and specific attacks by numerical simulations. We find that accelerated growth represents a convenient tool for improving the synchronizability of an evolving network. Furthermore, we show that not only network synchronization but also topological periodicity has robustness and fragility against random failures and specifical removal of the nodes, respectively. In particular, when ad hoc property is suggested in the evolving networks, we find that the deletion of nodes is easier to change network synchronizability and robustness compared to the addition of nodes.