Synchronized Firing in a Time-Delayed Neural Network

This paper studies the synchronization characteristics of a locally connected, planar network of (leaky) integrateand- fire (I/F) neurons after Hopfield and Hertz (1995). Hopfield and Herz showed that, with the assumption of instantaneousignal transmission, locally connected networks converge to periodic, synchronized oscillations. We verify these results as well as study their robustness when signal transmission delays are introduced. Our simulation results are consistent with the theoretical work of Gerstner (1996) but the simulation studies offer intuitions not apparent in the theorems. In particular, the simulations reveal that volleys of synchronized firing travel across the network in waves.