Balanced networks of spiking neurons with spatially dependent recurrent connections

TL;DR

This paper extends the analysis of balanced spiking neural networks by incorporating spatially dependent connections, revealing conditions for stable activity and exploring pattern formation when these conditions are not met.

Contribution

It introduces a spatially dependent connection model for balanced networks and derives conditions for stable firing rates in the continuum limit.

Findings

Stable balanced firing rates require broader external inputs than recurrent excitation.

Recurrent excitation must be broader than or equal to recurrent inhibition.

Finite networks exhibit pattern forming dynamics when balance conditions are violated.

Abstract

Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the spatial separation between neurons. In the continuum limit we derive that stable, balanced firing rate solutions require that the spatial spread of external inputs be broader than that of recurrent excitation, which in turn must be broader than or equal to that of recurrent inhibition. For finite size networks we investigate the pattern forming dynamics arising when balanced conditions are not satisfied. The spatiotemporal dynamics of balanced networks offer new challenges in the statistical mechanics of complex systems.