On Gaussian random neuronal field model: Moment neuronal network approach

A novel model is proposed to describe the rich dynamics of spiking activities of leaky integrate-and-fire (LIF) neuronal networks via the moment neuronal network approach. Different from the existing neuronal field model (for example, Wilson-Cowan-Amari model) which only takes the first-order moment (mean firing rate) into considerations, we develop a Gaussian random field to qualitatively describe the spatio-temporal distribution of the first- and second-order moments: mean firing rate, variance or coefficient of variation (CV) equivalently, and the coefficient of correlation (CC), of spiking trains. By this neuronal field model, we find out that the firing rate response with respect to the input may be not sigmoidal or even monotonic if the inhibition is stronger than excitation, which leads fruitful dynamical behaviors, in comparison with the sigmoidal response. In addition, within this framework, we can analyse the synchronisation propagation in the LIF neuronal network. We use our Gaussian random field model to investigate how the three key factors: the ratio between inhibition and excitation, the size of synchronous cluster, and the background firing rate, decide the stability of a synfire chain.