Abstract
This paper describes a neural field model for local (mesoscopic) dynamics on the cortical surface. Our focus is on sparse intrinsic connections that are characteristic of real cortical microcircuits. This sparsity is modelled with radial connectivity functions or kernels with non-central peaks. The ensuing analysis allows one to generate or predict spectral responses to known exogenous input or random fluctuations. Here, we characterise the effect of different connectivity architectures (the range, dispersion and propagation speed of intrinsic or lateral connections) and synaptic gains on spatiotemporal dynamics. Specifically, we look at spectral responses to random fluctuations and examine the ability of synaptic gain and connectivity parameters to induce Turing instabilities. We find that although the spatial deployment and speed of lateral connections can have a profound affect on the behaviour of spatial modes over different scales, only synaptic gain is capable of producing phase-transitions. We discuss the implications of these findings for the use of neural fields as generative models in dynamic causal modeling (DCM).