From electrical power grids and large-scale computing networks to flocking birds, understanding the behavior of networks containing dynamic nodes is essential in many fields of research. Network synchronization, in which individual nodes change their properties to achieve a global result while communicating only with local neighbors, is especially relevant. In a paper in Physical Review Letters, David Hunt, Gyorgy Korniss, and Boleslaw Szymanski of Rensselaer Polytechnic Institute, US, ask what happens in a synchronizing network if large time delays are introduced in the communication between pairs of nodes.
Hunt et al. consider a simple stochastic model in which each node in a network adjusts its state to match that of its neighbors, but with a uniform time lag in reacting to the neighborly feedback. For zero time delay, the authors confirm that the nodes in the network can achieve synchronization, and for some suitably large time delay there is a threshold value at which point the network becomes unsynchronizable. Hunt et al. discover that there are trade offs: for networks with large time delays, reducing how tightly nearest neighbors are coupled can restore synchronization of the network. The lesson may be that when there are large lag times in communication between nodes, reduced local coordination effort improves global performance. – David Voss