Low-dimensional dynamics of globally coupled complex Riccati equations: exact firing-rate equations for spiking neurons with clustered substructure

Abstract

We report on an exact theory for ensembles of globally coupled, heterogeneous complex Riccati equations. A drastic dimensionality reduction to a few ordinary differential equations is achieved for Lorentzian heterogeneity. By applying this technique, we obtain low-dimensional firing-rate equations for populations of spiking neurons with a clustered substructure.