Firing rate and spatial correlation in a stochastic neural field model

This paper studies a stochastic neural field model that is extended from our previous paper [14]. The neural field model consists of many heterogeneous local populations of neurons. Rigorous results on the stochastic stability are proved, which further imply the well-definedness of quantities including mean firing rate and spike count correlation. Then we devote to address two main topics: the comparison with mean-field approximations and the spatial correlation of spike count. We showed that partial synchronization of spiking activities is a main cause for discrepancies of mean-field approximations. Furthermore, the spike count correlation between local populations are studied. We find that the spike count correlation decays quickly with the distance between corresponding local populations. Some mathematical justifications of the mechanism of this phenomenon is also provided.