Simulation of planar I/F networks with delayed connections

Studies the synchronization characteristics of a locally connected, planar network of (leaky) integrate-and-fire (I/F) neurons after Hopfield and Hertz (1995). Simulations were conducted using both the Java programming language and the MatLab prototyping language in order to detect implementation errors. Further, two different algorithms were used in the simulations. The first method was a standard numerical simulation using Runge Kutta methods. The second method was an event-driven algorithm generalized from Campbell et el. (1999). Both algorithms yield the same results. Visualizations were included to make qualitative behaviors visually apparent. We replicated the original Hopfield et al. simulation results in which periodic synchronous firing emerged. The Java software displays the activation level of each unit in the planar grid in real time. The software also displays the number of units firing per time step. Since the software runs in real time, the user can observe a movie of the network evolution simply by running the simulation. The main result obtained is that when small delays are introduced, synchronized firing takes the form of a traveling wave across the grid. When axon transmission was instantaneous, it was possible to achieve complete synchrony, but when small delays were introduced the largest amount of synchrony possible as less than 10 percent. With larger delays, the synchrony disappears entirely