Fokker-Planck approach to the pulse packet propagation in synfire chain

We applied the Fokker-Planck method to the so-called 'synfire chain' network model and showed how a synchronous population spike (pulse packet) evolves to a narrow pulse packet (width < 1 ms) or fades away, depending on its initial size and width. The results of numerical integration of the Fokker-Planck equation are in good agreement with those of simulations on a network of leaky integrate-and-fire neurons. For a narrow input pulse packet, the integration of the Fokker-Planck equation requires careful numerical treatment. However, we can construct a precise analytical waveform of an output packet, which proves valid for narrow input pulse packets, from the stationary solution to the Fokker-Planck equation and a previously proposed approximate input-output relationship. Our methods enable us also to understand an essential role of the synaptic noise in the evolution, the peculiar temporal evolution of a broader pulse packets, and the irrelevance of the refractory period in determining the waveform of a pulse packet. Furthermore, we elucidate possible functional roles of multiple interactive pulse packets in spatiotemporal information processing, i.e. the association of information and the temporal competition.