On a Gaussian neuronal field model.
Can we understand the dynamic behaviour of leaky integrate-and-fire (LIF) networks, which present the major, and possibly the only, analytically tractable tool we employ in computational neuroscience? To answer this question, here we present a theoretical framework on the spike activities of LIF networks by including the first order moment (mean firing rate) and the second order moment statistics (variance and correlation), based on a moment neuronal network (MNN) approach. The spike activity of a LIF network is approximated as a Gaussian random field and can reduce to the classical Wilson-Cowan-Amari (WCA) neural field if the variances vanish. Our analyses reveal several interesting phenomena of LIF networks. With a small clamped correlation and strong inhibition, the firing rate response function could be non-monotonic (not sigmoidal type), which can lead to interesting dynamics. For a feedforward and recurrent neuronal network, our setup allows us to prove that all neuronal spike activities rapidly synchronize, a well-known fact observed in both experiments and numerical simulations. We also present several examples of wave propagations in this field model. Finally, we test our MNN with the content-dependent working memory setting. The potential application of this random neuronal field idea to account for many experimental data is also discussed.
Centre for Computational Systems Biology, Fudan University, Shanghai, PR China. wenlian.lu@gmail.com
Wenlian
W
Lu
Enrico
E
Rossoni
Jianfeng
J
Feng
D001921:Brain / Q000502:physiology*; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*